We decided to completely abandon MDF and made a panel from plywood, which we then covered with a frame of planed wood. We used regular pine plywood, which turned out great and was fairly inexpensive. We also had Krauta cut all the pieces we wanted. Three boards needed to be cut into various dimensions so the grain would run in the right direction. I think the guy who helped us got a bit amused by the job because he only charged us for 10 cuts. In reality, it was probably closer to 40 cuts. There was also no rounding on the frame, which worked out well. We just painted the edges of the plywood, which turned out fine.
For the frames, we just screwed and glued them and then filled in with putty. It looked good, too.
The biggest part of the job, in my opinion, was the planning before and, of course, the painting afterward. But the actual assembly and building went quickly. A few hours for all the frames. I would recommend it.