I have yesterday looked into the selection issue I wrote about and I found out, that it worked before the change. I have also found out, why it does no longer work and it is a complicated feature I have not implemented in the Change Geometry yet. Basically the edge indexes change completely when an edge is split and the selections are based on this indexes. I might be able to fix that, then the selections would just snap back to working state. I think that is, what I will look for next.
The second thing I did was to implement the incremental updates. Now the modifier seems to work again, I will try to give it a test ride tomorrow. Then I will see, if it truly works. But for now this thing is switched to the new base and should have some bugs less and be much more easy to extend. After I have fixed the edge issue I will try to add splitting of faces to the modifier. Then this modifier should be truly finished.