Electrical – Hbridge for ultrasonic transmitter

Rushing ...

Antiphase PWM per motor looks OK.

Disabling IC using EN lines will often create large motor spike - as long as internal IC catch diode rating is OK that's OK. Otherwise add external diodes to supplies.

What battery chemistry. What size?

AA Alkaline will often tolerate significant regeneration.

Unless battery is small physically or you want exceptional shelf life then NimH will be better than Alkaline. For very long shelf life LSD NimH are getting very good.

At AA size, energy density of NimH now equals or exceeds Alkaline and high load dishcharge characteristics are much superior so there is little reason for Alkaline.
At small cell size Alkaline MAY make sense.

I have not tried this
Answer is "seems like this to me".
Caveat emptor :-):

Motor inductance and resistance will set t = L/R time constant. But, very easy to put small resistor from motor to ground, apply voltage and watch voltage in resistor and thus current rise on scope. PWM period which is small compared to total motor rise time will (probably) be good.

I would suggest starting with a smaller H-bridge project first. The control of MOSFETs seems simple, but there are some subtleties which can easily bite you if you are not careful. When designing a smaller H-bridge project, it's not too hard to protect a circuit in such fashion that even if something goes horribly wrong it won't do much damage (and may very well not do any, though whatever caused the problem will need to be fixed in any case). This is useful not only from the standpoint of reducing the amount of time spent replacing blown components, but also from the standpoint of being able to figure out what happened. If something goes wrong in a 12V 30A H-bridge controller, it's likely to cause enough destruction quickly enough that it will be hard to analyze the pile of cinders and determine what failed first.

Beyond that, the reason companies make H-bridge controllers is that other companies buy them, and the reason that other companies buy them is that a surprising number of discrete components are required to safely and optimally control a MOSFET. If one is trying to control a MOSFET whose Absolute Maximum Vgs is 15 volts, and an inductive transient causes Vgs to reach 30 volts even for a microsecond, the part may easily be destroyed (the voltage required to destroy the part would most likely be around 20 volts, but one shouldn't rely upon it being above 15.01). Keeping Vgs below 15 volts may not sound hard, but factors like parasitic gate-drain capacitance can lead to some unpleasant surprises.