I went to adjust my valve lash, the nut broke loose fine (I mean to say turning the nut which is stuck to the screw broke the screw loose from the rocker), but the screw won't break free from the nut. This was the first one I tried and I haven't tried any others yet. I'll try soaking in pb blaster, but if I can just get new tappets at a reasonable price I'd prefer that.

I have a 93 Sidekick JLX 16-valve (180k miles)

https://www.megazip.net/zapchasti-dlya-avtomobilej/suzuki/sidekick-8588/se416-18299/se416-my-92-95-327705/cam-shaft-3809761

Go pick your parts from the link above - you can get the part number and do a google search, or you can just but them from megazip.