It is exactly this model:
Pro-Ject 1Xpression III
It has Ortofon 2m Red cartridge. Everything was factory mounted. He adjusted only the weight and anti-skating using no instruments, but little marks on the weight and the anti-skating dial.
Nothing else was messed with.
It'll skip on most records (and he does keep them nice n' clean) starting in the middle and increasing in skipping towards the end of the record.
He did notice it gets worse with records that last longer.
I'll ask for the rest of the details.