Have you tried finding software that can convert whatever the oringal file is into a .mts file? How did you transer the file back to the camcorder? Did you use the software that came with it, if it came with any?
Also, can you not stream the file from the PC to your TV.
I doubt you'll be very happy with recording from a flickering TV screen and I'm not really sure how good the projector on one of these things is. It might be usable more for quick viewing than for full scale cinema replacing, if oyu follow me.
Vizio M80-C3, Denon X6300H, Emotiva UPA5 (triggered), Wharfedale Pacific Evo 40s, CS, 10s, PC DX12 sub, Def Tech A60 Atmos tops, the internet, an ASUS ChromeBox running Kodi, a TiVo Series 3 and a Philips BDP7501 UHD . There's also a Wii, but we don't talk about that...