Doing 2 things at once
What you are proposing is not usually successful. It is best to do one operation at a time.
The powder will probably remain gritty. Although 680C is above normal slumping temperatures, it is not in the tack fusing range, so the surface is unlikely to be polished.
I am not sure why you are worried about a third firing. Taking the powders to rounded tack fuse will give them a nice surface, even though not flat. The glass should survive that easily, just make sure you do a good anneal after each firing.