I had a similar problem once and after replacing the alternator, belt (several times and brands), all brackets, water pump pulley, & crank pulley, I found that the snout of the crank was bent! SO, needless to say, check the run-out on the harmonic balancer pulley with the engine idling and watch for out-of-round movement from the harmonic balancer/crank pulley arrangement.
My symptoms were similar to yours, I would tighten the belt and then start the car and it would seem like it was loose again! I also could see my alternator bracket flexing when the belt went tight-loose-tight-loose, if that makes sense.
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1969 Camaro 383/365HP, B/W T-56 Six Speed, 12 bolt, Eaton Posi! 3.73, 4 Whl. Disc brakes, console w/Auto Meter gauge package, tach, clock, tilt wheel, Black Deluxe houndstooth interior, rear window defogger.