That's exactly the situation I was in with the last band I joined. Guitar player pushed the tempo to the point where the singer could hardly get all the words in. When I first joined the band it wasn't a problem. Basically, at my audition, everyone was sober. Before I joined the band, I MADE SURE that there were no major issues with alcohol and drugs, the guitard gave me his word that only a couple of beers were normally had during the whole night.
First gig after a couple of practices, went well.
Second gig went well.
Third gig, started noticing the drummer was not quite in the pocket. (my metering is considered excellent by all that hire me, which is why I get a lot of fill in gigs as well).
Fourth gig, keyboard player loses his cool because songs in the second and third set were getting progressively faster and losing their pocket and cohesion
2 months later, I had a chat with drummer to try to isolate the problem. Apparently, before I joined, the tempo problem was rampant, and the keyboard player blamed the drummer for failing to keep tempo. At that time I also had a chat with the keyboard player and I told him I had a plan to figure out why there was a tempo issue, because I was noticing the guitar player was drinking a little more each gig. Each gig we played, guitard would brag about what a great night he had, while the rest of us shook our heads wondering what was the problem. So, drummer and I focused much more than normal for the next gig, we stayed on tempo, pocket was perfect, and keyboard player was really happy. But, guess who had a really bad night?
Yep, Guitard.
The more he drank, the more he pushed the tempo. The guitard was quite loud, so drummer leaned toward guitard's tempo, throwing everyone off.
At that point, guitard was drinking 12 beers before even coming on stage. The band had approached him 5 times over the last 2 years to slow down on the drinking. By that time, I felt like I was had by the guitard. Then more problems. Pay was shorted because guitard spent his $125 at the bar, so he took care of the recieving of the money, and tried to tell us that the bar could only afford to pay us so much. Of course, keyboard player went straight to the bar owner, where bar owner told keyboard player that we received full pay, which meant guitard drank his share, and tried to put one over on us. It was that night that I decided that I was leaving. I told Keyboard player and drummer (singer was best friends with guitard and was just as drunk and stoned for the last few gigs) that I was leaving the band. They convinced me to stay for a little longer
2 more gigs pass, keyboard player was so peeved off at guitard that he sent me an email asking if I knew a guitar player as he was going to fire guitard. The three of us got together and decided that we would leave that band and form our own. We got a singer who showed impressive professionalism, my brother for a guitar player, and the rest of us, and left guitard and singer friend behind. We have been a very happy and decently busy band for the last year, while the other band, while still going, are getting very few gigs. Apparently, bar owners didn't want to deal with guitard because of their dislike for him.
If the story confuses you, go to wikipedia and look up ADHD.

kidding.
That's my story, I am sticking to it, but yes, I totally identify to what the OP is going through.