I have 2 LP 12s and have done upgrades on both. One started where you are and has been modestly upgraded. (The other done full-out including Ekos SE arm, Karousel, Radikal ...)
You could start with a Karousel bearing at $1,100 and $1k for a new base and Majik sub chassis. These would give you better grip and overall nicer musical presentation. If that's good stop there. .
Later on your could add a used Lingo power supply at around $1k and get a new arm. A new Krane is $1.8k or get a used one you like.
Also, Linn tables are very fussy and I would strongly recommend that you find a dealer to do the bearing, base, sub chassis at least. Those are installed prices anyway I believe.