Church Street United Methodist (which is on Cumberland, not Church
) parks cars on game day as a fundraiser for the church. You would need to plan on being there 2-3 hours prior to kickoff. It's much closer than the Credit Union lot off 17th. From 40 West you'd exit on the James White Parkway exit downtown, then exit onto Cumberland Ave. After you cross Henley St. the church will be on your left. After the game, you get onto Cumberland, make an immediate left onto Henley and you'll be routed to I-40 East back to Sevierville.
Another option, if you're early enough is to park either at Ruth's Chris Steakhouse or Calhoun's right on the river. I think Ruth's Chris charges $25, but they give you a $25 voucher you can use for food in the restaurant.
There are also lots of pay lots around the Strip and Fort Sanders. If you're not careful though you can be stuck in traffic awhile.
This game is going to have a light crowd. There will be lots of room in the permit lots but I doubt you'd be able to talk yourself into one of those.
Another travel option is to take US 441 to/from Sevierville. You'll have to follow the Henley bridge detour. If you do that you'll drive right by Ye Olde Steakhouse on your way out of town.