Thanks everyone!
Well, that's easier than i thought! I had previously drawn a circuit with one lm317, one lm358 and some transistors, but if i only need to supply one constant voltage, then i can get rid of the opamps, and the current limit could be one transistor with a current sense resistor that sinks the ADJ terminal to GND (the LM317 has a 2.2A typical current limit, and the transformer isn't going to be that big). The temp compensation is going to be a vbe multiplier under the voltage set resistors to get about -9.2 mV/degree C.
At first i was going to use the transformer originally included. It's 9v 200 mA, even if that means that the charging current would need to be only 120 mA, but when i tested the transformer, it had 9v rms with no load, and only 8.1v rms with a bridge rectifier, capacitor and a 100 mA load, so i think that i'm going to buy another transformer for this, or maybe some off-line 12v module. Well, at least i can use the LEDs and the plastic box...