Balancing NiMh batteries in series over a long term
NiMH has pretty high self-discharge. Read: the internal isolation is probably much lower than 10 MΩ. So those won't do anything.

I don't see any problems with NiMH cells in series – and the experience that all over the world, billions of battery packs are NiMH and NiCd series seems to indicate it's not a problem, too.

Notice that for battery applications, you'd design your LED system to be as energy-efficient as possible. Thus, you'd very much avoid having a voltage source higher than the forward voltage of the LEDs just to have a voltage to drop across series resistors – these really are nothing but wasters of energy.

Thus, you'd usually use a switch-mode current supply, which you can even buy as dedicated LED driver ICs – it's pretty common to e.g. find controllers that can take lower voltages and step them up for usage as smartphone flash drivers.

But basically, any LED driver really is just a switch-mode power supply in constant current mode. It's not really hard to build one that e.g. steps up 1.2V (a single NiMH cell) to something between 1.8 and 3V at a constant 30 mA to drive an LED with constantly the optimal current. Of course, you can also aim for higher voltage ranges, but usually, that implies that size goes up or efficiency goes down.

By the way, whether NiMH is the optimal battery chemistry choice is debatable: You usually use NiMH for high-current devices these days. For low current things, LiIon is commonly used – due to smaller size, lower self-discharge and also, often due to their higher voltage (something around 3.7 V, typically), which allows simple step-down converters for many applications. Charging is of course a bit more complicated, but that can usually be tackled by dedicated charging ICs or modules.