Replacing an LED Driver
It's a 25W continuous-current model (260mW, 28-87V)


No it isn't. You need to be careful about the details.


constant-current not continuous-current
260 mA, not mW.



  is it more important to match on wattage, or current, or both (or neither)


All are important but the most important is that the current be close to 260 mA. LEDs need a constant-current. You could choose a lower current and the LEDs would produce less light (fewer lumens, less brightness). If you chose a higher current driver the LEDs would have a shorter life, in the worst case, seconds.

It would be prudent to choose a driver capable of at least 87V and at least 25W. It doesn't hurt to be higher (so long as it is a constant-current driver set to the correct current). It shouldn't be less (though the old driver should have been specified to run comfortably well-inside its limits).

If you have a similar light fitting that is still working, it might be useful to measure the output voltage while the light is on. Alternatively measure the forward voltage across one LED and multiply it by the number of LEDs in series in each ring (look at tracks on reverse, they might be several serial chains in parallel).

If there is one chain of 24 LEDS, each 3V, you need a driver capable of >= 72VDC.

If there are two parallel chains of 12 LEDs, each 2V, you need a driver capable of >= 24VDC.


  I'm unsure if this has implications for whether or not it would be possible to use two 12W drivers in parallel


You are right, the two rings of LEDs are independent. You could use two 250mA 12W drivers.


  What's the best approach for getting this thing illuminating again?


Google for "25W 250mA LED driver"

The usual electronics distributors have parametric search