Individual LED are cheap, but fixturing is always a problem. At a wharehouse store I found 18W flush mount lamps for $14 after power company instant rebate. The LED took about 41V and the camp is 12V. I'm fond of these 150W boost converters on ebay that are less than $5 shipped. They boost up to 35V, limited mostly by the 35V cap. I could have removed the cap, I've been soldering for 40 years but these cheap thru hole boards with no lead solder make that risky. I would prefer just to bend the cap and break it off.
Anyway, I didn't do any of that. The toroid has enough space under it, if not it can be soldered and lifted. I added a separate seven more turns of wire with a high speed diode and filter cap. This was added in series with the output of the 150W boost converter. I added a 1K pot in series with the 10K pot on the board. This allows me to vary the brightness from 1/4W to 10W. That is almost too bright for the bathroom. Since I am no where near over current on the LED, voltage control is only on the boost converter. It does not sense the total voltage on the LED. I could have done that or sensed the returning current for constant current control. This is a quick cheap solution for some of those odd voltage LED.
I have some 91V MR16 spots that I will be trying that next.
Winding direction does matter a little. One way works better. Might as well do two winding and have full wave. I look for 1/3 of voltage to come from 12V, 1/3 from boost, and 1/3 from extra winding
When I get some time I will try rewiring the factory converter that came with the lamp. I should be able to use the output winding as the boost inductor.