i understand the halogen transformers will not successfully run the LEDs due to flickering and burn-out issues
If we're talking about oldskool transformers (the heavy ones) they output 12V AC at 50/60Hz so you need G4 bulbs that can take AC. They are easy to find, just check the specs. However notice a G4 bulb is quite small so there is not much room for a capacitor, which means they are probably going to flicker at 100/120 Hz. If this is a problem, get bulbs specified as flicker-free or read on.
If we're talking about "electronic transformers" (the flimsy and very light ones) they usually output 12V AC at a high frequency like 25 kHz or more which is usually also modulated by mains frequency. You need the same 12V AC LED bulbs, and they might flicker (or maybe not).
Some of these "electronic transformers" have a minimum load which might not be met by just a few LED bulbs, which then causes the electronics to misbehave and the light blinks or shuts off. I have some of these "transformers" in fixtures and usually they need at least one bulb to be incandescent.
If these "transformers" cause problems, a simpler solution is to replace them with 12V DC switching power supplies which are cheap and available. Then your G4 bulbs will get 12V DC and they won't flicker.