I hate riding alone for this very reason. I have only had 3 flats in 10 years, mostly due to fanatic checking of tires and pumping them to the highest pressure I can. People can tell me to take a class all they want, which I have more than once, but once I have to do something, I forget it all (and I have a good memory, but not for mechanical things). My last flat was just a couple of weeks ago. I was with Pata, so she guided me... I probably could have done it alone, as it wasn't the rear. This was from an obvious source, as I had ridden over glass earlier in the ride.
I truly get anxiety attacks over this. Since I can barely button my shirts or tie shoes, using tools is something akin to nuclear physics to me. One of my former colleagues used to laugh at me because I had trouble separating sheets of paper when I passed stuff out to my students.
As far as finding a group to ride with... I am sort of like the OP. Too fast for the slow groups and definitely not for the fast. I am happy with my speed, though. I did find a group, but now the "main" group is a little slow for me, so sometimes I try and ride with the "spirited" group, which I can usually hang on with. I like the people and it's social, so that makes a world of difference. I have 3 people I ride with, besides DH. Two are much slower than me. Pata and I are very compatible riding together and I thank this list for helping me find a riding partner I can actually ride with!