All good suggestions, thanks everyone. I think I'll try cutting a groove with a dremel bit to get a grip on it with a flathead screwdriver. I also thought I could try to pry the o-ring out and then maybe get a grip on the edges with needlenose pliers, but I want to stay away from the threads on the casing. I think all I need is a 1/8 turn to break it loose. Fortunately Mercury has this part number in stock, that was my biggest worry because I don't think the boat is usable with nothing holding that o ring in place.
I wouldn't drive the self tappers all the way in. Only enough to bite and hold. They also need to sit proud to be used as leverage.
It’s out! I went with a fine dremel bit made for engraving. My diesel mechanic also suggested a heated screwdriver but liked dremel idea better once I told him I had one. I replaced both sticks with new and kept the one used stick as a spare.
Actually @Blueone you were the first one to chime in with the heated screwdriver idea or the cutting a groove for a flat head screwdriver. So I think you got it!
@JamesT How did that happen? Do you think you cranked on it hard or did it really just break like that out of nowhere.
I didn’t crank it that hard. I think it was probably cracked already or some thing. These things are only supposed to be snug not super tight. I replaced the one on the other side too just out of an abundance of caution.