First brisket?
You have to let brisket set and cool before cutting it. Its really important, I know a lot of folks that will actually rest them in the reefer for 20/30 mins first. Mine sit at least 45 mins.
Second takes a sharp knife, not almost sharp, a sharp knife. You have to draw the blade across the grain and not try to saw it. The difference between a beautiful brisket and a terrible one is the slice. Pull a sharp knife across the grain.
Your brisket is falling apart tender and you're complaining, heck I'd hit it with some sauce and be tickled pink to have a sandwich! I would tell everyone I planned it that way.
I cooked a brisket today and as usual just started right in on it and had to back away and let it rest to slice it. Its not uncommon. Its like a pie, just because its out the oven doesn't mean you can slice it yet.
Congrats on your tender brisket, think of the folks who have not been here yet and had a tuff one.
Wasn't it a beautiful day to smoke today?