Done mixed cassette before. Initial results were as yours, with bad shifting; then redid the derailier cabling and recalibrated shifter, etc. Worked OK after that, not as fast shifting as normal cassette, but didnt skip cogs at least.

So my advice is to check the derailer/shifter and make sure its absolutely perfect cause even the most minor flaw is going to combine with the non-hyperglide cassete and mess things up. check the derailer hanger alignment, make sure the cable is perfectly lubricated, is the last 'u-turn' loop of housing the right size, etc...

If all else fails, switch to a non-indexed friction lever as your shifter. manual trimming solves everything, and really it was hyperglide that made indexed shifters possible so...implication is that if you mix your cassette and turn it non-hyperglide, you'd likely need to also revert to non-indexed shifting.