The floater frame for the gator mount may not have been the best solution, as you will see the rough edge, unless you try to flush mount inside the floater, and that's not the look most want from a floater, you want to have a bit of gap. Floaters are mainly used for canvas, thus you can see the wrap around the edges, at least the floaters I have worked with.
Part of the problem you may have had, or the framer is that they were cutting the print on top of gator. I have used Platine this way but not had any issues with edge flaking. But gator is not very forgiving. Foam core will probably allow for a less damaging cut. But again with a floater frame, you will see the edge.
With the prints you have mounted, you could consider a frame either wood or metal (metal is not always the cheapest), but wood frames needs to be joined and then you need a tool to mount the print into the frame like the Fletcher gun. Metal, you can assemble with no extra tools. All frames, should have enough edge to cover the rough edge of your cuts, not sure how big or long the scratches are from the edge but they might stick out from the edge.
You could also consider printing on an RC paper, since you were not considering glass (if a float frame was being used). The RC papers are a bit more durable and scratch resistant. Epson, Ilford both have several good ones. The surface will be more durable than the Baryta.
Just some thoughts for the future.
Paul