[Welsh Anorak]

I think you've proved that the problem is with the record head. It's possible that it's worn to an extent there's crosstalk, though a close inspection should reveal that. Aligning a three-head machine is of course more difficult than on a two-header, but the idea is to get the playback head absolutely correct then, using off-tape monitoring, align the record head.
You can rule out the erase head by erasing a portion of tape and check it's completely blank.