Is it possible to make hoop cheese out of acid-precipated milk curds?
I have also not tasted hoop cheese. All descriptions of it that I can find describe it as unsalted, pressed cottage cheese.

While you can definitely press out extra liquid from acid set cheeses, the proteins are not as firmly set and the texture is going to be very different.

I think you will find that using rennet is not much more difficult and opens a wide variety of cheese experiments.

Junket also provides quite a few recipes and I have had success with many of them:
http://www.junketdesserts.com/cheeserecipes.aspx
This recipe for cottage cheese uses the bacteria in (fresh) buttermilk to acidify the milk. Then with the addition of rennet a curd forms that is much firmer than what you get with acid alone. 

Making their cottage cheese recipe and pressing it into a hoop should be easy enough for you. I use the end cap of 6" PVC pipe with holes drilled in it as my mold and bungee cords for the press.

For an excellent page on home cheese production in general check out this page:
http://biology.clc.uc.edu/fankhauser/Cheese/Cheese_course/Cheese_course.htm