Tough to get engineering answers on a forum.
I really prefer cleats, rather than fixed eyes, for cruising. It gives me the option, when needed, to vary the angle of the bridle so that the cat can point into the waves, when the wind
and waves are not aligned. Your existing cleat placement would be fine, with good webbing chafe protection. I have had webbing chafe protectors, on a similar boat, last over 10 years.
If I were at a mooring
I would still stay with cleats, for a boat your size; the carabiners many use to connect to them are potential weak points; far weaker than the cleats, in any case. Anything other than carabiners, for me, would be too inconvenient. For a big cat I would consider eyes. But engineering the eyes so that they are stronger than the cleats (remember, this is a pull-out rather than shear force) is going to require a very large backing plate, probably about 10-inch dia, dependent on the lay-up. The eye will also see a cyclical bending force. I would think 5/16-inch would do, but I think 1/4-inch would crack in time.
Casanova bails require a front beam, which you ain't got. And I've seen cats where the front beam DEFINITELY was not engineered to take a forward pull; it could be pulled out that way (the tramp holds the beam in)!
As for the strength of the existing cleats, the answer is simple; there have been over 1,000 Geminis built. Has anyone pulled bow cleats out (I don't know the answer)? That is probably a better measure than any amount of arm-chair wagering. Not knowing the exact lay-up of the boat in that area, we cannot judge. If there are are no backing plates, add some; I would go with aluminum
All of the cleats I have seen fail have failed when the pull was upward (boat hanging from the piling). That places a terrible load on one end of the cleat, starting a tear. In your case, for a bridle, the pull will be slightly down or very slightly up (BIG waves) and so the load is entirely in shear. Failure would be very unlikely.
Why aren't cleats strength rated? Excellent question. It does seem that this is a safety
issue and there should be an industry standard, of which I have never heard.
2 bolts vs. 4 bolts? The ONLY cleat I have ever seen fail had 4 bolts, corroded in the hollow, and the legs came off. Also a bad bet for any sort of pot metal chrome plated cleat. Probably, it is academic, since reputable cleats will not fail. I would not use the cast-in bolt type; I can't remove or inspect the bolt, and there are many good through bolt designs. In reality, a 5/16-inch bolt is rated for ~ 5,000 pounds (breaking strength) in shear and you will have 2; any 8-inch cleat will rated for what you need, aluminum
or SS, and 10-inch is safe over-kill. 2 bolt cleats have bigger bolts than 4 bolt cleats.
No cleat design is likely to fail before the bolts, if in shear. However, if you have a lifting force, we simply don't have the product data to guess.
Don't use a short bridle; anything under 60 degrees really increases the forces; simple trig. For storms, use a long bridle to reduce the force (although, when the wind
veers, all of the force will be on one cleat, at times).
Personally, I think you are cool now, after you check those backing plates. I think I would go up one size.