To continue to use extra low voltage lamps either you will need to have a number of lamps all supplied from one electronic transformer or have a different transformer. The whole idea of the transformer was to extend the bulb life with quartz bulbs, so with maybe exception of bathroom, there is no point using extra low voltage with LED lamps.
Since the electronic transformer often also transforms the frequency as well as voltage there is often a limit to the extra low voltage cable you can use or it becomes a transmitter, there are made electronic transformers rated zero to something now, so for loading you could change them, however still a Mhz output and many G5.3 bulbs are marked 50 Hz, as to if really only to be used with 50 Hz I don't know, I think likely they would work OK with Mhz and the 50 Hz marking is because they know with a conventional transformer with is wire wound they can go all the way from zero to rated output. There are also DC power supplies and they are further divided into current and voltage regulated.
When moving from quartz to LED often the LED has cooling fins, so you don't get full 2 inches of light output, even 2 inches is small or 16/8" as with MR16, really you need more area lighting not less, there are other lamps like the GX53 which are slightly larger so likely will work better, but as yet only seen the adverts not seen one in real life. If the LED can be aimed at a white surface and you use the reflected light they can work well. However BAS is correct in the main they are simply too small to give out a reasonable spread of light, they may have the lumen but not the spread.
Within the lighting trade we have a host of names which no longer really apply to the product being sold, electronic transformer, electronic ballast, driver, MR16 and many others, they have retained the name of the item they replaced even though they do it in a completely different way. Why
winston1 has a bee in his bonnet with electronic transformers I don't know, as long as we use the word electronic in front of transformer it is not a problem. Driver is another story, traditionally a driver controls current but today there are lumps called drivers which control voltage.
I fitted 4 LED G5.3 MR16 lamps into my bathroom and slowly they all failed over around 6 months, second set cheap from Lidi have not had a problem, I will guess first set wanted a DC supply and second set happy with AC, but only a guess, however if you have option to move from extra low voltage (12 volt) to low voltage (230 volt) then I would, not had a single low voltage LED fail. And I would also look at something a bit bigger than 2 inch. Since very little heat from a LED they can be flush fitted it only needs hole for wires not for the fitting to go into. 
