Glad it settled down !
In my experience, a good 90% of the ' . . just can't get this $#**%(*# thing to stay in tune' problems are string related.
Wind the excess around the keyposts like spaghetti?
'Oh yeah, these strings have been on here since '87, I want that Jamerson tone!'
The retainer nuts around the shaft on the face of the peghead were loose.
The tensioner screws in the ears of the tuning keys were loose.
The saddles/tailpiece/bridge, etc., were loose.
The saddles hadn't been tuned to the string lengths (intonated) properly, or they still were set the way they left the factory.
The truss rod nuts were completely loose.
VERY occasionally, you run into the odd failing nut, frets gone wrong, or other mechanical issues from age or sloppy fabrication or the randon 'problem child' piece of wood, but MOST of the time, new strings and a proper setup kills 'it won't stay in tune' problems PDQ.
J o e y