I have had a lot of sucsess rejuvenating old Ni-mh and Ni-cad with simple self blocking oscillators. Got some really old Ni-cad 9v's off a mate, after 20 years in a multimeter. Would only hold 2v in one, 5v in the other. A few days on my Zenner tester boost circuit (basically a joule thief, with un-equal winds, that makes 400v from AA with low current) Used 2 flat AA's to fix the 2 9v's one has limited amps now, only delivers 100ma short circuit, but the Amp hours are pretty good, not much less than my brand new 9v rechargeable (I go through about 8 DMM batterys a week, in 5 meters, testing stuff) I have only charged Ni-mh a few times (don't have many), but some friends assure me they respond really well. They wont get hot either. Same for lithium.
The circuit I am using was designed to put a couple of hundred volts into a .2µf(ish) cap, for testing Zeners. so I used really thin wire (.2mm). so I could get the 400 turns I wanted on a really small toroid. It has lousy amp delivery, sometimes it brings the voltage of a battery up, and doesn't fill up the amp hours, if that makes sense. So I recover the voltage with zener tester, then put the amps in with my bought charger. Works really well. I will be doing a new one soon, with battery reconditioning and ordinary charging in mind. They work on any voltage too. I don't think they can overcharge stuff, but leaving one on would waste power. Not that they draw much.
There are a bunch of people on youtube re-charging old stuffed drill batterys etc. They have to be really bad to not recover to some extent. A lot of people experience faster charging too. Although I have not been able to re-produce that. I need to try thicker wire on my inductor before I can confirm/deny.
Tons of pattens and research docs available on the net suggesting square wave pulses are the go for most recharging (the flammable kind of lithium cell may be an exception, I know 2 people have had explosions, although they where pushing. The newer kind of Lithium rechargeable seems to be a lot less explosive from the reports I am getting). Freq is important. No one seems to know why, but some batteries like certain freqs better. I think its partly plate spacing, and partly to do with max current absorbance and partly recovery/re-gen rates. I could be wrong though.
I'd be inclined to have pulsed charging, and a pulsed LED output on the lamps. So 2 custom joule thief's. Although it might defeat your lesson teaching. I can get good light for a couple of days from a full AA, and have them just not go flat for dim light. The back emf from the inductor seems to excite the chemical recovery in the batterys, at around .5v, and they just don't get any flatter. just hover up and down by a few milivolts, a few times a day. Put one of those tiny solar cells from garden lights on the lamp, and make them charge their own lights. Go for homemade lead-alum-carbon batterys, and it will go forever. Like
Lidmotors forever light and forever motor.... With the cells you have, I could make a ridiculously efficient lamp. If you wanted to make them go flat quicker, you could go for a high voltage output oscillator, and run CFL's for a couple hundred ma from you battery pack.