For some reason my phone does not work right when I flash these Sprint roms I never have good service I get about 1g speed on average on stock rom I always have 4g speed also my mobile status say disconnect
your phone is sprint, uses sprint towers, just uses virgin mobiles network, also the stock phone lies about its signal all day long
the closest you could probly get at the moment would be the MK5 Stock Deodexed or odex roms, which if i recall correctly are just modified original stock VM 4.3 roms (jellybean)
as for the question of your thread, its impossible currently to have a 4.4+ VM rom unless someone builds it from the ground up, in which case they would need to use a source, and the only one available would be a sprint one since there versions is the one with multiple roms so far thruout its life (and here when i say multiple roms in its life i mean official ones)
also stock rom uses 5 bars for signal, non stock roms only use 4 so from the gate itll seem worse, also the custom roms measure the signal more accurately then stock does and recheck the signals more often, which is why most custom roms the signal seems to always bounce
currently the d2lte versions of roms arnt just sprint based since they include files for every single variant of the S3 meaning the d2lte has files for Sprint, VM, Boost, and probly Tmobile, att so on and so forth (actually the att parts probly a lie as i believe there model is the 745 or something), the only thing im unsure if they have is the apn setting for each carrier included but as ive been seeing ppl say they no longer needed the fix i would guess there working on it
your mobile network state should say connected tho, are you using the APN fix after flashing the roms, or are you only flashing the roms zip???