A radical cut down is the best way to encourage fresh growth from the base and a bushier shape, so I would go for it and cross your fingers. A sprinkling of alfalfa pellets around them and then mulching on top with fresh compost should give them an energy boost to bounce back with new growth.

During years of drought, I kept old hybrid teas alive with the barest amount of water. When restrictions on water usage were removed, I tripled the amount of water and doubled the amount of organic fertilizer. Results were amazing - green leafy roses with thick stems over 8 feet high with dozens of good size blossoms. Water makes a huge difference. Lavish amounts of compost applied after January pruning and in mid summer enriches the old soil.

Advice from a master gardener in the area (southern California). was very helpful during heat waves and Santa Ana winds, as was the practical advice in the superb book "Showing Good Roses" by Bob Martin.

https://www.abebooks.com/9780971013209/Showing-good-roses-complete-exhibitors-0971013209/plp

You may want to build a watering basin (with walls of good new dirt from the garden center) around each old rose, then fill it with an inch of water once a week as well as running your drip irrigation system. Or adjust the number of drippers to get far more water on the roses than on neighboring succulents.

@NollieSpainZ9 I think I will go for it. You prefer to use an organic material like worm droppings as your compost? Honestly, during the Summer I found that a pure nitrogen fertilizer like Blood Meal was rocket fuel for roses.

@apple_pie_order What about building a small border wall around the edge with stone and just filling with a few inches of mulch? That should be enough to preserve the water they already get.

I have long since thrown timidity to the wind and adopted a kill or cure attitude to roses. There are so many gorgeous roses out there just waiting to take the place of a lanky, poor performer!

I am no spray but will use any organic material I can get my hands on - alfalfa, seaweed, fish emulsion, leaf mould etc. My dogs are way too fond of digging up and eating blood and bonemeal so I avoid that, but whatever works for you. Funny you should mention worm castings as I only recently discovered a source of really excellent stuff. The compost I use is a good quality ericaceous mix, which helps to buffer my alkaline soil

A nice dirt (mud pie) and stone border wall could hold water in a basin. Plain stones will leak water. I usually mulch with compost that's essential to get wet to do any good for the soil and plant. Dry mulch will certainly slow down evaporation from the soil underneath.

Please post an update when you are ready, maybe in a few months after new growth appears.