Gary, I have yet to meet an established (old and neglected) rose that did not recover from a very hard pruning. The roses you describe sound like modern repeat-blooming types, so I believe you’re safe to cut them back to 1 to 2 feet tall and they will regrow. There are always dormant eyes on the canes and at the base of the plant, ready to start new growth when needed.

A hard pruning of an old plant is generally rejuvenative, so this is an opportunity to reclaim these roses and build them up with renewed vigor.

If these are actually ”antique” types that bloom once in Spring (no repeat) then you can still cut them back, but you will sacrifice this year’s blooms. If these are once-bloomers, you can wait until they’ve finished blooming and then cut them back.

Thank you, Paul. Spring has already sprung here in Central California. There don't appear to be many buds developing so there isn't going to be much to lose flower-wise. Everything leafed out quickly before I had a plan but I'm going to go ahead anyway. The plants seem to be really healthy otherwise.