and am debating buying a set of high-capacity NiMH cells and stuffing them in there.
Be aware that its WATTS that make light. Not volts!
The D4 has 6V of drive. It therefore must draw twice as many amps to make the same watts as a C8, which has 12V of drive.
All things being equal, you want higher voltage and lower amp draw. Why? Because its amps that heat up the wiring and cause arc wear on switches and such.
Second, you will need TWICE as many mah from the D-cells as from the Cs, since you have twice as many Cs.
I'd go with the C8 (non-rechargable), and get a set of 4500mah NiMH cells for it and a charger. The bulbs in mine are labelled as 13 watts. It will draw 1.4 amps. With 4500 mah capacity, and using 80% of them, you will have a burn time of about 2-1/2 hours.
That ought to take care of you for a day of diving, at which point you can (of course) recharge.
A D4 with a 5.8W bulb will draw about the same current, so with the same 4500mah cells (but in "D" size) you'd get roughly the same burn time. BUT - the light will be a LOT dimmer! 5.8W is nowhere near 13 watts!
Get the C8 and refit it with the 4500 mah NiMh cells.
(You can also get a higher-output bulb for the C8, intended for use with rechargable cells only, that has an output of 18 watts. Note that the C8 also has TWO lamps, which gives you redundancy in case the bulb burns out - very useful! With the 18 watt bulb and 4500mah cells you get 1.9 hours of burn time, which is still pretty good - and may be enough for a day's diving as well.)
One thing to be aware of is that with rechargables you need to charge the night before you dive. All rechargable cells have an inherent "self-discharge" rate and as such you can't stick the light in a closet and expect to use it in a month without experiencing significant capacity loss.
If you keep the regular lamps in the C8, you can still use alkaline disposable batteries in an emergency (you forget to charge the NiMHs!) which may be worthwhile.