Have now bodged on a Digispark board (ATTiny85) with code to control the LED modes, so I can now have a 100% mode (yay!) and any other dimming levels/flash patterns that I want. Had to run the micro at 1MHz to get the power consumption down as the puny zener-diode-based supply wasn't man enough for the 18mA the Digispark wanted. (The original PIC-clone draws about 0.6mA, for comparison).
The total dissipation at max brightness is now up from 1.8A to about 2.2A.
Next step: lower the current-sense resistance to push more current through the LEDs.