Is there a huge need to keep your current address as your permanent address? State income tax avoidance, healthcare ...?
You can also get a 2nd home mortgage and keep your SD address as permanent. It would probably require more down payment, and maybe an uptick in rate! The other issue with a 2nd home could be your insurance on the home. It used to be null and void if the house has been vacant for maybe 30 days or more. Other ways around that though.
Being homeless for 5+ years may even qualify you for 1st time home buyer programs! Don't give up. If you have found an area that you want to buy, then get a Realtor and use his resources. Good luck.