Besides a good tape path cleaning for the capstans and pinch rollers, it will be up to the technician to remedy the tape skew.
When I get a "new" deck, my sacrificial tape for testing is a pre-recorded Michael Bolton - and it has lasted a long time. Damn!
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It's good to see your NAD 6300 arrive and in action. I have a few vintage Marantz components I've been collecting for an all-Marantz stereo system - excluding speakers.
Nando.