Nimh's can deliver high currents so in theory it'd work, for a short while.
Take care on the kind of amp you use, high frequency noise from the switcher can make an amp unstable and blow up.
The tl494 is a veritable chip and ought to do the job.
I like to use etd series transformer cores, theres an online calc to work out windings, the issue with ferrites is not to saturate them.
Also as you found out the supply voltage for the smpsu controller might be an issue, maybe a little joule thief type circuit just to power the tl494 might be the way to do it from a low voltage supply.
You can get fet gate driver ic's, but they are critical on board layout and bypassing, I tend to use a pair of transistors from the chip to the fet, if you get a fast switching time dissipation from the fet is lower.
This is an interesting project, keep us posted.