Broken Upper Rudder Gudgeon

I have a restored '73 H14 Hobie that has been working pretty well but broke my portside upper rudder gudgeon in a tack this weekend (a bit tough going getting back in with 18 knot headwinds). I was able to remove one of the two original screws holding the gudgeon (with great effort-very frozen). However, the other screw has broken off inside. Was thinking about converting to a one piece. Lots of info on the H16 but not sure if it'll fit a 14. The other option would be trying to drill out and re-tap the hole which would be my overall preference. It sounds like there is a big aluminum block so I could simply go at a different angle if I can't drill at the same trajectory as the original. Any advice would be appreciated.

Ouch, Yes there is a 1/4 in thick al plate in the transom that the gudgeons screw into. You should be able to get the old screw out with the right sized extractor. I tried to put the one piece gudgeons on my 14. You have to cut them off. but what i ran into on my 85 was that the screw holes in the transom were all at different angles (not perpendicular to the transom) and i had several of the screw heads that interfered with the rudder pin lobes and i couldn't get them tight. 3 were above or below the lobes so i couldn't move the holes. I would get all the old screws removed, but before you take the last one out make sure the plate hasn't broken loose from your transom inside. Run a tap thru all the old screw holes to clean them up and then check the alignment of your screw holes. if they are perpendicular to the transom you will probably be able to make the one piece gudgeons work.
The H16 guide works on the 14.
I installed the new 2 piece gudgeons but be aware that they are not as thick in the lobes as the old style and i ended up using a 1/8 in nylon washer as a spacer to help take out the vertical slop.
I have a photo of the plate in the transom but i have never been able to get the insert a image thing to work

Thanks for your reply. Very helpful. To be clear, I removed 1 of the 2 screws from the upper gudgeon but the other SS screw is broken, headless, stuck inside the transom. got about 4 threads out with the head. It's pretty likely that my drill will find the softer aluminum and the SS will stay inside. I will first try to drill and tap a new hole as close to the old one and perpendicular so the screw heads don't affect the rudder assembly. Would love to avoid cutting down a 1 piece but that will be my fallback. Good news is that I have an '83 that I bought for spare parts so I wont have to deal with the newer, thinner gudgeon and upsize the rudder pin (also picked up a hand impact drive, which should help).And since you were so kind to offer advice, please LMK if you need any spare parts for your '85! I got it for the sails/battens and dolphin striker, really.