Q

This is essentially clearing a slightly tipped Pacman game screen of pink dots. This can be very frustrating though because after being 99% done, one pink dot is unreachable.

My recommendations is to pour 5-10 balls in the two center holes on the top, and watch to see which pinkies they clear out. The balls you have to worry about are all in the center area--the corners where your balls won't normally hit. There are 6 of them in the center, 3 on the left of center, and 3 on the right of center. If your initial pour of balls doesn't clear the pinkies in the courners....
I found that you can very carefully do a tiny ball draw right next to the pinkies in the corners and you can get them with slightly enlarged or odd-shaped draw balls. Don't worry about anything else until you get those 6 out of the way, working from bottom up.
Once you have those six nasty corner balls out of the way, send balls down from the top clearing everything else out. Be especially careful about the bottom left though--I would pour balls down the left side, and then sometimes drop a stick down the left to force the pile on the bottom to get the ones above the normal ball pathway.

If you go that way, it should save you some frustration from restarts.