You said your snake goes up instead of down when it hits the tee. Is the tee installed upside down? That would cause some problems. The grade being uphill doesn't help either. When its clear it will still drain but you will always have standing water and crud which will not clear and builds up faster.
Go buy a fernco (Rubber coupling with 2 worm clamps) and cut the main line 3-4 inches back from the tee, disconnect your p trap and pull that line out. You should be able easily feed in the snake and get it to go down the right direction. If it works your out $10 and if it doesn't the plumber will be in there anyway.
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