What you should do (if financially possible) is buy a small tract of land in a rural area. Most counties in TN have ZERO zoning in areas that are outside of city limits. Do some very minor improvements, like a driveway, get it mowed 3-4 times a year, and go for it. Putting in a driveway and improvements will get you a physical street address.
Most UPS stores offer "suite" addresses as well, along with forwarding services. In your shoes I would find a list of stores online and actually CALL to make sure they offer that service.
Get your driver's license moved and register to vote using the physical address of your property. You will break even very quickly in Tennessee's low tax environment.
Driver's licenses may be renewed ONLINE in Tennessee, for an extended amount of time like 15 years. They are good for 5 years.
Property is cheapest in west Tennesse. (flat, but nice people.) Look in Gibson, Crockett, Haywood, Fayette, Hardeman, McNairy. Madison county is where Jackson is and it would be more expensive. The tier of counties along the southern border as far east as Marion county are very rural, also more hilly and prettier. Along the northern border, all the counties between Sumner and Sullivan are extremely rural, more rugged country, very very pretty. The next tier south of those is also very rural.
You won't find the services and amenities ANYWHERE that you have in Michigan, but you will find, as you know, very little in the way of taxes, also.
You will also find it an absolutely beautiful state, especially in the spring and fall.