Route from Yellowstone to Grand Tetons

Hi Again--just looked at the Yellowstone NP website and the Grand Loop will be closed from Old Faithful to West Thumb for construction beginning Sept. 2. We will be staying in West Yellowstone and moving to Grand Tetons (Coulter Bay) during that time. I asked this question before and you guys recommended going through the park and taking Rockefeller Parkway. Do you still think this is the best way to go with 5th wheel trailers even if we have to go around through Fishing Bride and Lake Village or is there a better way to avoid the closure? Your advice is always appreciated. Thanks