There are decent trailers around to start a fresh build with. I just don't see the best use of your resources in breaking down what you have, rebuilding on it and selling the tent only part. I think Semi Hex is right, sell the whole thing. You'll probably come out in better shape financially and someone else has a complete (mostly) camper to start with.
So I would recommend abandoning the wings if it's a keeper after. Why? I presume you want to set up the trailer for the RTT and to me that would include a mount for it, but also storage, work station, kitchen that is somewhat accessible while the RTT is in use. Does that sound like something the present trailer is going to work for? If not, another reason to trade.
Then there's how capable the trailer is on the trails you anticipate, plus maybe the ones you'd like to do. Do you want something more worthy of where the tow vehicle can take it? Add-on tent(s) to add protected space to use the facilities is something else that you may want to consider with the RTT. They're great for sleeping, but it's the addons that make them livable beyond that unless you limit camping to fair weather only.
Of course, it also comes down to budget. It's not the best season to sell a trailer, but it's a good one to buy and you can afford to go ahead and look for something more suitable. While ours is not for sale, I can highly recommend the M101 CDN like ours.

Lots of builds with them that have stuff rolling out the back of the trailer or lids that tip, depending on how you camp. That's probably toward the overkill in terms of chassis, but they're pretty unbreakable. Other set-ups I've seen make use of an old (or new) utility truck type body. They do set up higher and usually heavier, but have LOTS of room if you're the type that hauls it all to the woods or like to keep your options open, so to speak. So different ways to go and worth looking around for what's out there to consider.