With most of the top 8 national rental car companies (Alamo, Avis, Budget, Dollar,
Enterprise, National & Thrifty), as you've checked, the minimum age to rent (with an underage fee) is usually 21 or older.According to E-Z Rent A Car.com, renters aged 18 - 20 years old are allowed to rent from their corporate locations with an underage surcharge of an extra USD $35 per day
The only other possible exceptions to this rule would be for active duty military personnel or federal government employees. You can also check to see if the company that you work for has a corporate account with any car rental companies. Many larger businesses and companies will contract rates with their preferred car rental company(s) and will negotiate a lower minimum age to rent for their employees.
If you own your own business, you can also check into setting up a business account with one or more auto rental companies and seeing if you can get a program that will allow you to get a rental car under 21 years of age.
Read more about Business Car Rental Program Benefits
You may also have some luck by searching outside the larger, big brand national rental car companies regarding rental car under 21 policies.
I did a bit of checking and found this information about Rent-A-Wreck:
"Usually, Rent-A-Wreck requires renters to be at least 18 years old, (25 for some locations). For consumers under 25, a credit card is usually required for payment and the rental rate may be higher. Renters should get in touch with the individual Rent-A-Wreck car rental location to check their particular minimum age policies."
Their location info is:
Rent-A-Wreck of Nashville 201 Donelson Pike Nashville, TN 37214
Although they had no websites, you may also want to check:
Discount Rent A Car Serving the Nashville Area
Tennessee Car And Van Rental 2408 Lebanon Pike Cir Nashville, TN 37210