Similar but not equal. All the losses that subtract from 100% efficiency will work in the opposite direction as a dynamo.
So if the motor is 75% efficient under those conditions, then its 100% efficiency speed (unloaded) might be 4000rpm and it would draw 0A. You can roughly crosscheck by monitoring its stall current at the same voltage : in this case, it may draw 24A at 0 rpm. (The motor regulation would be 1000 rpm for 6A, or 167rpm/A, or 24A for 4000 rpm)
If that's the case, then you have motor constants of 4000/20 = 200RPM/volt, and a winding resistance of 20/24 ohms = 0.8333 ohms.
Given these values - and they are based on my guess of 75% efficiency for your motor - the open circuit voltage would be 3000rpm /(200rpm/v) = 15V.
And if you drew 6A from it, you would drop 5V across the winding resistance, so you would see 15-5 = 10V across your load, instead of 20V.
The bridge rectifier would then drop 2* the diode drop (say 1.4V for silicon diodes) giving 8.6V DC. Schottky diodes or synchronous rectifiers can improve on this, but probably at more cost than is justified for such low power.
Measure the motor regulation by running your motor at different loads and measuring both speed and current, and cross-check by measuring stall current, and you can arrive at the likely dynamo performance for your actual motor.
I assume this is a 2-stroke engine.
So you want to use the stepper to deliver power, and hence maintain a relatively constant angular velocity as the power stroke finishes, and continue through compression until the IC engine fires and generates power again.
That should be two fixed points on each rotation, though it might take a bit of care finding where those points are (hence, partly, my comment lower-down about using a high-resolution sensor)
You could sense those positions with two Hall switches and magnets attached to the shaft. That is how some motor vehicle engines sense shaft position.
Hall effect sensors should be good for more than 1000 rps, e.g. 60,000 rpm.
Most reasonable microcontrollers could track 4,000rpm with much better than 0.1% accuracy.
However, driving the stepper, with only 12 steps might be tricky to set up, and drive. 12 steps is 30 degrees per step, which is quite a lot compared to the motor's cycle. This sounds more like a BLDC motor than a stepper motor.
Even with 8 step micro-stepping, the angle is quite big. AND, 8hp is about 6kW+, which is quite a lot of power to switch and control.
Further, to maintain near-maximum torque, the movement of the magnetic field needs to track the motor's rotation reasonably accurately. I'd be tempted to go for 'overkill' and use a high resolution rotation sensor. That might be Hall Effect, like something from AustriaMicroSystems (AMS), or something optical.
Edit:
Texas instruments (TI) have some useful documentation and videos on 'Feld Oriented Control' (FOC) for BDC motors which may help. A web search will find this stuff.
TI have some affordable (sub $100) development boards for low-power (10W?) control too, as does ST Micro, and I'm sure, others. There are 'fast/easy start development kits' for motor control. I haven't used them, but they claim to have control software 'ready to go'.
Summary:
Sensing the shaft position for the IC engine might be a relatively easy part of the project.
Best Answer
You'll need some kind of control system, one problem that I see is the bigger motor also generating voltage in the smaller motor and creating a positive feedback loop. Because of this control theory will be needed to find a closed loop system response that is stable.
In my mind it would be better to use an encoder and use the position output from the encoder to control the larger motor.
If you do need an opamp to control the motor (also look into PWM control), the output can be boosted with a bipolar output stage