Is it exactly 22 hours? or could it be off by a few minutes?

If it's exact, then he could get a servant to try a bottle, let's say, every 30 seconds and then put a time stamp on it. In the 2 hours each servant could try about 240 bottles of wine. So the king would only need around 4 servants to try the wine.

100.

Each slave gets 10 bottles to test a half-glass of (so they don't just die of alcohol poisoning and invalidate the tests), then whichever slave dies you throw out the 10 bottles they drank from, with only a 1% loss of wine which I think would be an acceptable loss.

Of course this is purely from a numbers standpoint, it's better no-one dies at all. So a better technique is to ask which of the slaves has a chemistry degree, then send them to work testing all the bottles for whatever poison it is. So this could vary the number of slaves needed, depending on how many happened to be educated, but more would be better and save more time.

Why he needs 1000 bottles ready to be drunk within 24 hours is odd though; you could just get one slave to test one bottle, and if he doesn't die the King can get pissed on that bottle for 3 hours, assuming no-one else is joining him.