No one aswered me so I will answer myself in case anyone else needs this information.
I am still confused. I want to replace BOTH my screws.
Do I order two "8030346 SCREW W/NUT ISLAND GUDGEON STUD 1/4-20 x 1" PH17-4 W/ NUT SEIZED", or do I need to order a different part number for the top screw?
They are the same.
Also, is anything to be gained by using the newer 3 hole gudgeon even though I only have inserts for two screws on my TI? Looking at my current two holer, it looks like a 3 holer would have more surface contact with the boat even without the third screw.
Yes or no, depending on which gudgeon you have. If you have the gudgeon in Tom's picture, there is no advantage. The molding around the holes is even with the edges on my old gudgeon but are recessed by ~1mm on the new one so they don't make contact anyway. However, my two hole gudgeon is not the same as Tom's. They made at least three versions: Like my original, like Tom's and the 3 holed version. Tom's is shaped the same as the 3 hole version, but as you can see in the picture below, mine is not. I think there is a substantial benefit in upgrading from mine to either Tom's model or the 3 hole version due to the width difference.
Due to the way my bottom insert is bulged out (see snjsander's pic below), I also filed away some of the bottom hole molding so the gudgeon edges would contact the hull. Then I cut a gasket out of "Fel-Pro Rubber-Fiber" gasket material to make a good all around firm attachment.