My Nak 505 sounds like its going thru a phase shif

The pinch roller is skewing the tape due to tape residue build up. What your service dept is probably doing is replacing the pinch roller OR pulling it off it's bearing, cleaning it, turning it around and putting it back on (most likely). If your Nak uses two rollers, then the one on the right (as you are facing the machine, nearest the take up spool) is the culprit. If you are handy, you could remove the cover and door and do this yourself in about 30min time. Another thought is that they may be 'rotating' and reversing the two pinch rollers. Teac used to make a wonderful pinch roller cleaner/conditioner which left the rollers very soft and prevented the skewing that you are experiencing (which is caused by the residue left from your tape). Lighter-fluid will also do the same thing. I usually dilute it when cleaning the rollers.
Hope this helps.
Best,
Norman

You will also want to keep the capstan clean. This is the small rotating shaft that the pinch rollers bear against. It should look nice and shiny- any texture means its dirty.

Dirty pinch rollers can be caused by tape shedding and the rubber of the roller perishing. The deck is old enough that you might consider having the pinch rollers replaced.

As far as the cassettes shedding oxide- put them in a warm car for a day- that will allow them to get rid of some of the moisture they have picked up from humidity over the years. Then they will shed less.