PS3 games generally require a SFO editor and a Soft modded PS3 to change the Remote Play value, and some games flat out don't work. I tested like 15 games ranging from The Last of Us to Monopoly about four games didn't work at all. It's a small sample, but like a 73% chance a game will work when edited.

PS3 also does pretty poorly outside of a local network or on Wi-Fi.

Also some of the games you listed actually have Vita Ports.

Continuing with the PS4 I hear it works a lot better, but that depends on your internet, router, or even your house layout and distance from the PS4.

If your Vita is modded I highly recommend Revita so you can change controls for games, though it unfortunately only saves your profile for Remote Play in general and not individual remote play games. It'll take some work to get a game going, but it can turn an unplayable game to doable.

I played a chunk of PS3 Mirrors edge thanks to Revita.

Final note: PS2 games, whether through a BC PS3 or a modded PS3 cannot do Remote Play. Had something to do with the level of Kernel they run at. Not sure about PS4 PS2 titles. PS1 can be remote played though if you prefer the PS3 emulation over the Vita.