First of all resistors aren't used to regulate voltages of any significant consumer.
There are several reasons for that, but the most important ones are that the resistor itself is dissipating all the dropped voltage and consuming power. That will have an impact on the battery life. The second equally important point is that resistors drop voltage but they do not provide voltage regulation! The amount of dropped voltage is dependent on the amount of current that passes through the resistor! So if you have a motor running with no load, the resistor will drop one voltage but when you put load on the motor, the resistor will drop higher voltage (assuming your power source can provide enough power and 9 V batteries aren't the best option here, especially for motors).
You can use a potentiometers and rheostats to obtain variable resistors that will give you different speeds for a motor, but the main problem with them is in general potentiometers are designed to dissipate small amounts of power and when adjusting voltage with a resistor, you'll have large power dissipation on the resistor which makes potentiometers unsuitable for directly adjusting voltages of large loads.
Also note that THERE IS ABSOLUTELY NO WAY TO USE A RESISTOR TO INCREASE VOLTAGE!!! This one is important! I'd not go too much into physics behind that here, but I think that the idea is basically equivalent of truing to produce oil by pushing your car backwards.
On the other hand, the linear voltage regulators behave like a special type of resistor which automatically adjusts its resistance (within certain range) so that the output voltage is (more or less) constant. They too dissipate the extra voltage as heat and aren't a good solution for large loads especially on battery power. Voltage output of linear voltage regulators can be controlled (on some regulators) and you can use them to control speed of a motor.
Now about the voltage drop using H-bridge: It's a bit more difficult to explain, but the main point is that when analyzing voltage coming to a motor you have basically two voltages: voltage in a single moment of time and average voltage over some time. Usually with H-bridge circuits, you're providing full instantaneous voltage to the load, but you're constantly turning the load on and off. This happens so quickly that the average voltage will look like a voltage lower than the input voltage and that way you can provide speed control for a motor by changing the time during which the motor is provided full voltage and time during which the motor has no power. The main advantage of that approach is that you are wasting very little power for voltage regulation. The transistors in an H-bridge will usually have low on resistance and when they're on, they are fully on and when they're off, they are fully off, so only little power is dissipated by them.
Another way of getting the right voltage is to use a switch-mode regulator. They are often more complicated and require more components or are more expensive if they come in same form factor as linear regulators. The good sides however make them very interesting. They can (depending on specific device) decrease or increase output voltage compared to input voltage and they waste very little energy as heat when doing so. They produce more noise on the output than linear regulators too. Anyway as far as motors are concerned and as far as I can see, there is no major benefit to use of switch-mode regulators compared to say PWM, since motors can survive short exposures to higher voltages with no problems at all (as long as the time is short enough so that the current is below the maximum rated current for the motor).
Now about that PWM motor controller: In general you'll need at least two wires to control it: ground wire to provide reference or ground voltage and a signal line. So if you're going to use an Arduino, you'll need to connect the negative sides of the controller's power supply and the Arduino together and you'll need to find the controller's signal line and drive it with PWM from Arduino.
Next, I see you mentioned stepper motors. They are usually controlled not by traditional H-bridgees but by stepper motor controllers. Basically a stepper motor has several inputs which control individual windings on the motor. You need to provide power to each winding in turn so that the motor will rotate. The speed is controlled usually not by voltage directly but by the amount of time each winding is energized. So to increase the speed of a stepper motor, you "simply" need to switch between the windings faster.
Now a little bit about the 9 V batteries: They are in general a poor choice for running any significant consumer because they are usually constricted by having 6 1.5 V cells connected in series. The cells themselves are very small and have low capacity which limits the capacity of the entire battery. This also affects the maximum current the battery can provide and since motors are significant consumers, the lifetime of a single battery will be very short. Some better options are to get say 6 AA (or C or D) cells and connect them in series for much higher capacity and higher maximum current. Another option (which could be much more expensive if you don't have the appropriate tools) would be to get a 12 V battery, such as a car battery and then recharge it or to get a 3 cell lithium-polymer battery or to get 6 cell NiMH battery.
You probably need a motor-run capacitor to make the AC induction motor work properly. It does say 8uF on the label.
Also, I really, really doubt the first motor is a stepper motor. It states 100V, 50/60 hz. 100V is the Japanese line voltage standard, and I have never seen a stepper motor with a specification in hz.
Edit Ok, the first motor is a 4IK25RGN-A. This is a 1/30th horsepower AC induction motor.
Realistically, neither of these motors are appropriate at all for a servo system. They both look to be fractional HP induction motors.
You can control speed of an AC motor with a variable-frequency drive. However, VFDs (and induction motors in general) do not have much 0 RPM torque, and don't provide control of the actual motor position, just the motor RPM.
Really, you need a brushed servo-motor, or a brushless AC servo-motor (or even stepper motors). All of these use a different mechanism to generate motion then an induction motor, which is actually a rotating transformer.
Best Answer
First we need to look at the uncertainties before we address possible solutions:
Are there two motors in use or one - it could be either from your text.
And, is the 40A for two motors in use or one?
You say " ... motor was spun ..." - what does this mean? An unloaded motor is rated at 2.7A, at normal load it's 27A and max power = 68A.
Where on that continuum is "was spun" ?
You need to describe the nature of the load and your application. Whether it is possible to decrease input power to the motor to within battery specs and still meet your requirement is unknowable to us as you have not provided enough information.
What is the mechanical arrangement?
What attaches to the shaft(s)?
Why do you need to run it at that power?
Why can you not run it at lower power?
Do you use a motor controller or just connect the battery to the motor directly?
Please supply battery model and brand and very ideally a internet link.
What else can you tell us that may help us to help you?
Mechanical:
Changing physical gear ratio inside the gearbox is a mechanical task outside the scope of this form. It is possibly possible, but more likely not to be. Doing this depends on the gearbox design. The manufacturer and/or user community will be able to comment on this.
If you are using or can use a belt or chain drive externally you may be able to change the ratio of pulleys or sprockets used to reduce speed and increase torque.
You MAY be able to move the motor back from where it is mounted so there is miore room and add an inline speed reducer - maybe 2:1.
Electrical:
You can PWM the motor(s) to limit battery current to 25A continuous this will reduce power to probably about 25/40 = 65% of that at 40A but maybe not. Motor efficiency rises usefully with decreasing current but it is not certain how it will run at 25A mean under your load.
Depending on facytors such as PWM frequency and duty cycle, motor imp[edance and more PWM may reduce peak moptor current to mean current or may still cause peaks greater than motor continuous maximum. So, if you use PWM yiou will ideally add capacitance to the PWM input = battery output that will supply the PWNM pulse currents while limiting mean and peak battery currents to no more than the continuous maximum rating.
Battery rated maximim continuous output is 25A.
Based on what you say the unseen by us data sheet says you can run it at 40A for 30 seconds followed by the rest period for 70A in the data sheet - ie at the 70A ratings. You MAY be able to run it for longer safely or with a lower rest period. Or not. If you provide a link to the battery data sheet and tell us the brand and model we may be able to tell you more. Maybe not, but without that it's a guess at best.