I agree with kknowlton's suggested route. We also have a heavy fifth wheel of 35' and have driven both routes, with the route through the park being shorter. With the speed limit and likely traffic, it'll take you a little longer, but take the time to enjoy the drive.
2011 Bighorn 3055RL, 2011 F350 DRW 6.7L 4x4 Diesel Lariat and Hensley TrailerSaver BD3, 1992 Jeep ZJ and 1978 Coleman Concord Pop-Up for remote camping
Dave & Renee plus (Champ, Molly, Paris, Missy, and Maggie in spirit), Mica, Mabel, and Melton