I'm not asking how to make the drummer better, how to replace him, how to tell him he's not good enough, or any of that.
I just noticed you said you didn't want advice on how to make him better, just how to stay sane with the problem.
And then I gave all this advice about how to make him better.
If you want to just learn to cope with it, try the following:
1. Do some thought control where every time he does something that disturbs your peace, you replace that thought with the size of the crowds, how everyone is committed, and how nothing is perfect.
2. Reflect on your upcoming gig schedule and CD that is selling well, and how most local bands never get to the same level you guys are at.
3. Find some kind of fun way of getting the musical quality you need, perhaps by calling some other cats to come over and just play. Even music greats do that now and then.
I play with two people who are NOT at the top of the scene in our town. The drummer can't solo well, the piano player plays so sparsely sometimes our best songs don't sound right (I can think of one song that really gets me..it's my best composition but it sounds the worst because she doesn't have the right feel under it). But I get along well with them, and they are willing to go out and do non-profit work, support my volunteer activities, and play my original music. Further, if I throw corporate level work at them, we get good reviews, notwithstanding the deficiencies I see.
So, I look at the whole, not just the pieces. I have to say, this band, with these budding musicians is my favorite one right now because of all the other non-musical factors. Granted, there is some good musical stuff, and the musicians tend to want to be together, practice when we have a gig, and bring their own written music to the band. And they follow me without much question, taking whatever pay or gigs I throw their way.
Look at the whole, not the individual pieces.
I wouldn't abandon helping the guy become a better musician though. That way you can stay in the band without all this mental discipline above.