There is very little we grow "not as perennial."
Sweets are my ground cover and yams a climber in both st Petersburg Florida and the oregon coast.
It is a challenge to grow enough calories to be self sufficient. Especially without grains. Sweet potatoes are my easiest solution. As a ground cover they provide virtually unlimited pot greens. I trim walkways to harvest greens.I pull tubers as needed.
I plant them in compost rich soil.
Top dress with compost regularly. Turn the chichens loose in the fall when the greens start to fade or if bugs get too vigorous. Find good ethnic markets for seed stock. Purple, red fleshed, orange fleshed, white. Some sweeter some more savory. There are hundreds of kinds grown around the world.
I had maybe 3-4 sweet potatoes which didn't look very edible, which I planted in a bed in the back yard, and now the vines/leaves cover about 40 square feet and vines are growing up the supports for the porch roof.I haven't tried digging them up though, I believe the vines just root wherever they hit soil, so I'm not sure there would be much in the way of tubers, I rarely water them and this area is very dry.
I'm not quite a lumberjack, but that's OK, I sleep all night and I dream all day; I'll coppice trees, I'll grow my food, and compost poo and pee! With a well and off-grid solar, it's a permies life for me! https://www.youtube.com/watch?v=FshU58nI0Ts
Yep, I use sweet potato as perennial ground cover. I chop it all back maybe three times a year and find the random sweet potatoes at various stages of ripeness. If you want a continuous tuber production, then you're better off putting a little intention into it; put several starts in one spot; that will make harvesting a lot easier because you have a nice clump of them in one place. When you do harvest, then just stick another bunch of starts in the ground and repeat the process. This isn't really perennial, but continuous cropping.
I feel like its a trade-off: if you want the fertility benefits of perennial ground cover then you settle on just a meal every once in awhile; if you want something more substantial then you go with the continuous cropping method. You don't get something from nothing though, so you choose your benefits from any single element: soil fertility or yield. In my circumstance the sweet potato is ground cover in a food forest, so my main production is from the fruittrees.
We have a very small garden in front of a townhouse in Cebu Philippines. There's a compost heap or thick mulch on an area 2 feet by 8 feet, where we grow a few rambling things with sweet potato being by far the most prolific. The shoots are harvested every couple days for salad greens and stuff to go into soup. Being extremely well fertilized, they grow fast and aren't tough or bitter. There's no plan to dig up tubers, since they are so cheap at the market. But it's really handy to have greens just outside the door.
I grow sweets as a perennial, but I do occasionally dig the beds up and start anew. It gives me the opportunity to add soil amendments. But I do have a couple beds that I pretty much ignore for 2 years or more before I harvest them for livestock feed. So at least in my location, it's a perennial that can be in the same spot for quite a while, if I wish.
Pests.....yes, that can become a problem from time to time. My number one destructive pest is whitefly. If they visit one of my sweets patches, they can really knock the plants hard, causing all the leaves to fall off and most of the stems to die back. Eliminating sweet potato whitefly has been impossible so far. So what I do is harvest everything that's above ground (feed it to the livestock), rake off any mulch and incorporate it into a hot compost pile, and add 2"-3" of compost atop the ground to act as fresh mulch. What grows back usually looks good for another year or longer.
There are several other nasty sweet potato pests here in Hawaii, but the whitefly is the only one that has found my farm so far.
I've noticed that some varieties are better at being perennial than others. Okinawan shows up everywhere if I leave even the tiniest root nodes behind. Old Maui White isn't as aggressive, but it has proven to be a stayer in the perennial department. But other varieties don't seem to rebound as strongly. So perhaps which variety one chooses to grow might be important.
I haven't done a lot of experimentation with sweets, but I have learned that there is great variety among them. Some have short vines, others are longer. One I've grown was so aggressive with 30' + vines that I had to eliminate it. It was overtaking everything near it. Some are bunching types with the tubers right under the mother plant. Others produce their tubers away from the mother plant. Some make large tubers, others make small. Some produce almost no tubers at all, but massive amounts of leaves and vines. There is lots of variety in sweets.
It's never too late to start! I retired to homestead on the slopes of Mauna Loa, an active volcano. I relate snippets of my endeavor on my blog : www.kaufarmer.blogspot.com