Do you have a copy from before this conversion? It is safer to select all your verts and hit connect. Converting your geometry to patch may break things in unexpected ways. Also, make sure you don't have other UV channels with splits in them.
I know this isn't a technical solution persay, but I always try to hand triangulate non-planar(within reason) faces. If you have a quad that is very non-planar and you're worried about how your app/exporter/etc will triangulate, do it yourself! There should be an easy way to select non-planer(with a certain threshold)…
The handness problem only happens if your middle vertices (along the seam) are not split uv-wise. That's what I meant with if you split the uv-vertices there, there is no problem. That is you can select each "half" of the divided plane in your uv-editor and move around freely. The middle vertices still share positions and…