Oh wow that is dinky. I can’t seem to find anything smaller than 17mm. DX and intl-outdoor (IIRC) used to sell smaller driver boards years ago. I think a lot of them were double stacked boards though. Some sanding is the only option outside of salvaging a driver from another light.
If NiMH regulation is still your goal you have limited options. I have no first hand experience with any of these, I am willing to bet most have visible PWM. Like the TG06 and your OEM driver.
https://www.fasttech.com/products/1612/10001750/1127407-12-aaaaa-5-mode-800ma-linear-booster-led-flashligh
https://www.fasttech.com/products/1612/10002000/1143101-1-2-aa-aaa-1-18650-1-mode-1a-led-flashlight
(Sold out)
https://www.fasttech.com/products/1612/10001715/1134800-1-aa-aaa-5-mode-550ma-linear-booster-led
Craig has this low voltage driver here:
http://www.illumn.com/leds-drivers-optics-mcpcbs/led-drivers/700ma-boost-aa-driver.html
If the noise and inductor whine is whats bothering you, you could try potting it… (Sorry I don’t know the proper word for it.) Potting is a term guitar players use for submersing guitar pickup coils in paraffin wax to mute feedback and noise from loose coil windings.