I had a strange idea. I heard of software which from my understanding uses UDP to transfer files decreasing the overhead found in TCP packets.
If my app requires TCP and
TCP's problems are in its algorithms, not its headers.
You certainly could implement the TCP algorithms on top of UDP. That would effectively be the same as tunneling TCP datagrams inside of UDP datagrams. But all this accomplishes is to add a few more bytes of overhead to each packet, and require another endpoint to unwrap the packets.
UDP itself is just thin shim on top of IP: its a convenient way to access IP packet switched networking without having to dive into kernels or receive special handling from routers. The main reason to implement reliable transport on top of UDP is to get away from TCP algorithms in favor of something more efficient. FileCatalyst was mentioned above as one company which does this, and my own company Data Expedition, Inc. does so as well.
So you could implement TCP algorithms on top of UDP, but you wouldn't want to.