I'd keep the 4 cells and switch to a buck driver... there's enough meat in that pill to be bored out to take nearly any size flashlight driver on the market.
I wonder if adding a few more amc7135’s might help with 4 Nimh’s. Raising the vf of the led from the extra current and lowering the voltage difference. There should be more battery voltage sag too at a higher current.
I have a 4D mag, 12x7135 driver and XML that I run on 4xAA Eneloops with no problem.
Cool. Now try it with 4 D cell NiMh and see what happens. Make sure you have an extinguisher or at least a bucket of sand nearby.
I do have one that runs fine on 4D Nimh’s but they are very tired and low quality cells. If i remember correctly they where about 1.1v under a 3 amp load. It does depend on the voltage sag greatly of the cells used.
Most new D Nimh will hold around 1.20v or so at a 3 amp load from the graphs i have seen.
I would be surprised if the 1/2D NiMHs are much better that four Eneloops. Those Chinese 1/2D probably don't have all that much reserve capacity. You really need to be able to test under load and see what your voltage is before you know much. Without that, it's guesswork. I do a lot of that, guesswork that is.
If the driver is really getting too hot, then help cool it off. Before you put it in the heat sink, cover it with Arctic Alumina or at least a good thermal paste, so there is no air gap in the driver pocket of the heat sink, just solid thermal compound in between. Then cut a piece of thin copper and cover those exposed chips on the top side, using Arctic Alumina to hold it. Cut the copper like a large washer, where it covers the chips and sticks out close to the outer diameter of the heat sink. Make sure that there's lots of Arctic Alumina so that just like the other side, there's no air gap anywhere. That should be enough.
What buck driver would work good in there? I thought they needed alot more voltage than just 4 cells