Just guessing, but... either your passenger side headgasket has developed a breach between an oil passage and a cylinder (EXAMINE the gasket; also, is there any oil in your COOLANT?), or you've had a valve guide fail on that same head.
120k is not a lot of miles, but it's not a little either. Since the heads are off, might as well have both "re-conditioned", including a valve job.
You should've run a compression check before the heads were pulled, but I agree, the rings USUALLY last a long time in this engine... OTOH your oil consumption was EXTREME.
If you get the recon'd heads and new headgaskets (and new STUDS) on there and then find out you still need a ring and bore job, you're not really out much, except some labor.... and a new round of headgaskets...?
Please report back--we all learn from each other's repairs.
Edit: just noticed the part about getting it for $1k, i.e. you're not the original owner... so let me say 120k mi. is not a lot IF THE OIL IS CHANGED RELIGIOUSLY... sounds like you might have an abuse victim, where the oil (and filter) were NOT changed much, if ever

... in that case ANYTHING is possible, incl. entire bottom end rebuild!! Might just wanna get a junkyard replacement.