I've actually been looking into this recently for myself as I'm looking to grow red and sweet potatoes, and from everything I've read, do not bother with potato "towers". The vertical methods you see in videos don't really work because potatoes won't produce tubers more than a certain height above the seed potato. They'll keep growing green leafy stuff as high as you want to keep mounding dirt, but there won't be any/many tubers in there when you knock it all down. In the reading I've done, it actually wasn't uncommon for people to end up yielding FEWER potatoes than they seeded with.
I would look at the classic methods, or perhaps the container methods. In fact, there are some fancy 10-gallon containers with flap doors that let you reach into it on the side and apparently harvest a few here and there while they're growing..... I'm not sure how well that would work, but it is an interesting idea.
Unless you're eating these every single day, you would need what.... maybe one or two containers per month you want a supply for? That's pretty easy to find space for, I'd think.
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