You're asking 2 different questions here. One in the title and one in the actual post.
1. GME funding - Misunderstood by almost everyone, including most PDs and many GME offices. If you match into another residency program, you will have decreased, not NO, funding. It will be on the order of 60-80% of what the institution would get for a fresh grad without prior training. And since many institutions are well over their CMS GME funding anyway, it will likely be a minimal to non-existent issue, again, assuming the PD and GME office understand how funding works and don't just cash the checks.
2. Prior training - Rads reuires a prelim year. It can be in anything. Most do IM, GS or a TY. You've completed an entire FM residency. You're fine.