As long as people who already have the original frame can’t get these new modified frames, I like this suggestion. Otherwise it would be a bother for completionists depending on how and how often they were re-released. Portraits also take space in the inventory and works towards the inventory limit, so that’d be another reason for only being able to have one of them.
If the exclusive frames are made available through the emporium, the frames could have a small shilling mark on them. If they are made available through subsequent events, they could have a number on them. You got the frame the second time it was made available, it would have the number 2 on it for example.