The initial problem is probably that the new load of LED lamps combine for too light of a load for that electronic transformer. It's not a true transformer, but an oscillator, so if new load is too far off the load it was designed for, they just don't work correctly. If you added a couple more of the LED lamps the flicker would go away, but being track lighting, I imagine that's not an option.
Question is - do you think the 36kHz is causing the SMD rectifier and diode device to get so hot?. The LED lamp only draws about 220 mA and remember it does not have any problems when run off a 12 VAC / 60 Hz. What would you suggest? I could get a lot bigger diode and stuff it into the lamp just fine. I just don't know what frequency limit full wave rectifiers are good for?
The 36 kHz is on the low end of frequencies in this application, so it shouldn't be causing an issue. But being that you got the LED lamps on eBay, it's possible that they contain slow components that don't switch fast enough to handle that frequency. For your bridge setup, a bigger diode won't help, you need a faster one. A bigger one would dissipate more heat of course, but it would still heat up over time. At that frequency, on with a T
rr of 200 ns should be fine. As far as a frequency limit for full wave rectifiers, I'm sure there is a practical point where you can't find diodes that are fast enough, but 36 kHz is no problem.
Also, it's a bit unclear, did you use a current limiting resistor in your cobbled circuit? That would help too.