First congratulations on the new camper.
It's better to have a flat on the TV than then tt. We had a simular situation a few years ago. Everytime we go camping with my brother's family it's an adventure. He got a flat, at a major interstate interchange just a few miles from home, in a road construction site. And of course he did not have all the tools to change a tire. He was following me, so I had to circle around and pull in behind him.
Double check that you have the tools to change a tt tire. Lug nut size maybe different than the tv. Also your TV jack may not be addiqate. I carry an 18 inch breaker bar and three sockets, with that combo I can change tire on a all my cars and my two trailer. Same combo is in my TV and my every day car. It takes very little space, and is strong when have to jump on it because a tire shop over torqued the lug nuts.
No help with the bedding. We have queen our htt. They are an odd size, but a regular queen fits fine.