Oh yeah, definitely have a go. I first tried budding at hort.college where I used a heap of New Dawn (another doddle to propagate). For sure, I didn't do a comparative trial with other rootstocks so I couldn't in all honesty state whether using ND was any sort of improvement compared to the more usual laxa or even on their own stock but it was fun to do, all survived and I felt absurdly proud of myself.
I was going to have a stab at rooting and budding at the same time, using cuttings of canina but events got out of hand and the timing passed me by.....but next year, I am keen to see if a double operation has legs because I do like this sort of messing about......

Both multiflora and Huey have been used widely as stocks in Texas rose production, so those should be OK for you. Fortuniana may also work. One of the benefits of using a tried and true plant for root stock is it has already been tried with a variety of different scions (the bud inserted into the stock) and is more likely to be compatible with more varieties of roses. You MAY run into some incompatibilities using more modern roses, or not.

Another benefit of using tried and true stocks is they are known to accept scions easily. It might be possible some garden roses may not.

You also need to take how easily the bark lifts from the cambium, making it easier to accomplish budding, into account. Known stocks tend to be some of the easiest. But, give them a try. Kim

Fortuniana has been found satisfactory in limey South Florida soils, some of which are heavy marl soils.

I think the commercial use of multiflora rootstock in Texas was in East Texas sandy loams rather than the type of soil you describe. Multiflora has trouble taking up iron from alkaline soils.

Ah, yes, that makes sense. Commercial rose fields in TX are in the east, e.g. around Tyler, where the soil is red sandy loam & more neutral. The area has good pine tree growth.

On the mid coastal soils here (black clay "gumbo", oak scrub prairies) chlorosis is definitely a problem, though.
I recall a number of HTs, probably distributed from Tyler growers that were on Dr. Huey. I just don't recall them being very long-lived in the 25 yrs+ I was raising roses there. Almost all the roses I moved inland were own-root ogrs.

I'm assuming the problem is increased in this new-to-me area of limestone hills & want to try some budding on stuff that may do better. Plus I just want to fool around with budding. Thank you all for the responses