Because you said you've tried almost all the free apps i mentioned. I assume you've tried Gun Bros and Contract Killer. Gun Bros is fun to beat imo, and if you don't want to spend money on items and stuff, just befriend other players that has the stuffs. While Contract Killer is good for passing time since it's energy limited type of game. These to games is shooting genre and free XBLA.
There's also curtain shooting Danger Wing. It has funny dialogues and storyline. I'll reccomend you to play while on bus or train, since it only use touch control, not tilt, so you can play using one hand(right or left, yes they have that UI option).
For adventure, i think there's many, idk if you've tried text based games like Wizard Choice or Bump, has strong storyline and good reading and games(yes, it IS game). Or you can try platformer like Cartridge. For TCG, Cabals is solid one. For tower defense my pick is BBB: App-ocalypse, even if you finish the game, you can enjoy buying all the items in store or competing in leaderboard, they also release The Zombie Situation (idk tho if it is the same dev, need confirmation).
For games, i think you better consult game section, sharing your picks and better support. That is what i can reccomend, hope it helps.