NICE!
I used to have one of these decks. It was given to my by my dentist (odd, huh?) who was about to throw it away, along with about 45 reels of Sony PR-150 tape that had AMAZING dubs of classic rock records.
When he said he was about to trash it, I said "no you aren't" and picked it up that same day! I spent the next year and a half on my spare time dumping the tapes to my PC, into CD-format audio. To this day I'm still in the process of researching the music, and chopping up these massive WAV files into tracks, for enjoyment on other medium.
I did experience the issue that you're experiencing with the machine. At first, it would play and then slow down to a crawl after about 10 minutes, until the tape stopped. I took it to a local vintage electronics shop, and they managed to lubricate it and clean the belts and moving parts enough to bring it back to life to the point that it would play a tape at the correct speed consistently all the way through.
But I continued experiencing the issue with the play lever not latching -- it was intermittent, and eventually it was stay. I never pursued fixing it though.
That's a really cool website -- I wish I had seen it before when I still had the deck