I was lucky...
 

I was waxing my outdrive and noticed it was very loose. I found the port side pivot pin sheered completely. I was lucky the drive didn't come off. Changing the pin should be easy I thought...I was wrong. All four stainless bolts that hold the pin to the gimble ring broke off. I hope I can get the remaining screws out but I am not to optimistic.

Should be able to have them drilled out, just gotta keep the drilles from walking. Maybe use the sleeve as a drill guide? Wonder if you can just rotate it 45* and drill 4 new holes, or would that effect the rings strength?

I am going to try and drill them. I sanded them flush and will get some good bites and try drilling them to relieve the pressure. I will try and easy-out and if that doesn't work I use a high speed pencil grinder with diamond bites and try to remove enough to allow a pick to dig it out.

I thought about drill 4 new holes too but like you I wonder if it would be a strength issue. I hate not knowing...

Invest in a good set of left-handed drill bits. Good things to have on hand for situations like this.
Good luck.

I never have much luck with easy outs on small bolts if they are really struck. They work by wedging themselve tighter into the drilled hole of the screw. Seems usually that in itself just expands the thin wall of the screw even tighter against the threads of the ring. I'd soak it real good wtih PB blaster too.

Try a local machine shop, often times what these guys will charge to fix a mess like this will supprise you. To them this is childs play because they have all the right tools to do it right. I have at times created my own little disasters, turned to a local guy that does this chit for a living, and walked away convinced I was nuts to spend the time I did trying to fix it myself. They might be able to drill it out and then retap the threads or install some heli-coils for you. Would be where I would turn for sure.

What I have found over the years is ... I can fix this, cause I am pretty handy! I get started and for whatever reason things just aren't going well. This turns to pizzed off. Which then turns to the "larger hammer will fix this theory". Which fails! At which point I turn to someone that does this chit! Which usually turns out well! At which point I come to the brilliant conclusion that life would have been much simpler had I just done that in the first place!

Well I took and good look at this and listen to the advice given and got lucky so far. I had a drill bushing made to fit tightly in the new Merc pivot pin. I purchased some very good left hand drill bits, drilled slow and use a lot of lube to keep everything cool and so far I have two out. It has taken about an hour so far but it's winter so no rushing needed.