Yes, you could put new pieces in-I have some spray Dykem that I put on the metal, put it behind the holes, scribe and cut it about an 1/8" larger, grind to fit and Weld. As you pointed out, the partial problem is the shrinkage caused by the Weld-you can planish the Weld flat with a Slapper and Dolly. I generally will put enough tacks to hold the piece, then grind the Welds down to within a 1/16" (front and back), planish and do it all again, a few Welds at a time. This will stretch the Metal back into shape without letting the shrinkage get out of hand-if you do too many at a time it can be a bear to get the Metal flat again.
I am going to fill in the Holes in my Dash also, however I have decided to smooth the entire Dash, so, I am going to cut out what I don't want and put a new, one piece patch in-the reason I am going to do it like that is that I want a clean unwelded area to bore the new holes in without dealing with the welded areas (which are harder to drill and a Hole Saw can cut cleanly)-