I have to say, it sounds like you really botched the first repair attempt, especially if you tried to put a heli-coil in with part of the broken bolt still in there. You should have never tried that.
I'm going to give you a little broken screw 101. First using a sharp center punch try to get and starting point as near center of the broken screw as possible. Using a sharp, 1/8" drill bit, drill a pilot hole as near center as possible. Start slowly and angle the drill as needed to get the bit in the center. Use max drill speed and light pressure as you drill the center straight down, If you use slow speed, the bit might bite into the metal and break the bit off in the hole. If the bolt is has work hardened, you might have to use a slower speed on the bit to get it to cut, just be extremely careful if you do. Getting that broken bit out will open another whole bucket of worms because it's too hard to drill so has to be broken out. Once you get your pilot hole, being careful to feel when it goes through the bolt, and you don't drill all the way through into the lower unit. Now you want to go up to the next larger bit and start making the hole bigger, still angling the drill as you first start to help work it toward the center of the broke bolt. Once you get the hole large enough you can start seeing the threads on the bolt, us a small, pointed punch and start working it between the aluminum hole and the steel bolt, breaking, crushing the bolt into the hole. There are easy-outs you can try once you get close but not those spiral tapered, they only make it tighter at the top, it has to be a straight shank, again, be extremely careful doing that because you can break the easy-out off and back to the same problem of trying to break it up to get it out.
Unless there is a fair amount of good metal below where you have already botched that hole, you WILL NOT be able to use heli-coil to install the factory size bolt back in. That's why I said you might be able to install an insert, they require a little larger hole that a heli-coil and you might have enough metal left to hold one of those. The only option for a heli-coil is going to be using one larger than the factory size. Your heli-coil options are probably going to be a #16 or #18 machine screw if you can find one or something in a metric that is just a little larger and drill the pump housing out a little. I doubt you have enough metal to go as large as and 5/16" bolt. That's why I said and insert is probably your best option if there is not enough metal left below what you have screwed up. If by some chance there is enough, then do the heli-coil deeper and use a longer bolt. Just be care you don't drill through into the gear case. If by chance you do, don't fret it too bad, just make sure you put a dab of silicon in the hole before you install the bolt to seal it. If all else fails, you can just drill the OEM hole deeper, getting below all the botched hole junk, using the water pump housing and plate as a guide. If you do, make sure you go a little at the time with grease on the #7 drill bit to catch the metal shavings, so they don't go into the gear case. Tap it to the with a 1/4-20 tap, if that's the size of yours, again, keeping grease on it to catch the shavings. Then just use a longer bolt. Let me say, I've never done that with an OMC gear case, so I don't know how much metal is below the OEM hole and there might not be enough to get a useable length of threads. So you are on your own if you try that one.
I've never use this but I know a couple of people that say it saved their butt, so might be worth trying if you see no other options. Loctite Stripped Thread Repair Kit, 12.9mL, Gray Form-A-Thread 236382 | Zoro
Like I said, there are tons of ways to repair it but I have done this crap for most of my 77 years so I have a little more experience on how to fix an "O-Sh**!"