It might take a couple of year's experimenting with your soil and light conditions. You could make a raised bed with loose soil inside your fenced area using broken down pallet material and make a trellis from the pallets rather than mounding and allowing the vines to spread all over the place. (Will you be doing this for your Kyoto Red carrots anyway?" I have grown them over the past couple of years and my regret is that I did not start them earlier. 2 more weeks of growing would have resulted in more substantial tubers. They were also a pain to dig up. I had some problems with mice or ground squirrels eating the tops of exposed sweet potato. I think I have about 30 pounds harvest total. Since you need to import your water or store your rain water in a cistern that might be an issue.
My experience is with Baker Creek's Carogold and Korean Golden sweet potatoes. I think I prefer the Carogold, but the Korean was more productive. I also tried their Okinawan and Hawiian sweet potatoes, but they did not do well for me and were not well recieved by others so I moved on. (Purple, white, dryer and more enlongated than U.S. Varieties.)
Orange Variety Covington is supposed to be good. 100 to 115 day maturity. more disease resistance and more regular shape. I have not grown it though. (Do a "Brave search" on covington for more info.
Good luck!
Picture from the August Garden....Fig trees in 5 gallon pots, Sweet Potatoes, Pumpkin vine, painted scarecat that did not scare.

I do plan on trying them eventually and I can grow Irish potatoes just fine. Grew some nice ones for a couple of years after adding to the beds some humus that I had scraped up with a grader blade clearing off prior forest to get grass to grow. First year I harvested by pulling the plants out by hand, taters and all. Smooth and blemish free and I think I hit the 7 lbs of potatoes from 1 lb of seed potatoes mark that’s considered highly productive.
Soil is clayey loam, brownish yellow, a bit heavy. It doesn’t take a whole lot to turn it brown and/or fluff it up. Doing that to a great depth is a different story. A long story.
I do have some depth though. Top soil is 12” where the high tunnel is and gets deeper towards the road which is 300 foot away. Got a over an acre of that. Corner post out by the road was easy to dig. Went 30” before it started turning orange/red clay.
I’ve never had luck with sweet potatoes: The plants seem to grow fairly well, but don’t produce more potatoes. IIRC, I started them in early April. The soil they were in was moderately light, but did have composted Hickory debris* in it, so, the juglone content may have dinged them. Do you suppose that they would grow in Ohio River sand mixed with light garden soil? I could go get some sand. (It is very fine, almost a silt.) I don’t know what variety my plants were, last go-round they were just marked “Sweet Potato Starts”. The “meat” is a typical yam-like light orange in color. Definitely I can trellis them.
*We have lots of hickory trees, and a few walnut trees, one quite large as the “mother”, so, spots without juglone and / or Hickory debris (especially) in the topsoil are hard to come by. Walking outside today with the stiff breeze that came up was “refreshing” and a good way to get hit by a falling walnut (in the husk) or hickory nut (same story). One of the walnuts that plunked down near me had a husk diameter of 3”!