The standard route on Moran is the CMC route, starting at the CMC campsite. But, this is not "car-to-car", which would be starting at the Jenny Lake Loop Road, and either walking/running around Jenny & Leigh Lakes, or canoeing the lakes (which is the usual mountaineer's approach).
Erik Sanders describes the multi-sport (bike, swim, run) "Picnic":
The Moranic or Mount Moran Picnic is a multi-sport effort involving biking, hiking/scrambling (up to about 5.5) and swimming. There are a few variations of the swim route but described here is what I consider the most logical swim variation, considered the Beasse route. Since the typical approach to the CMC face is by canoeing across Leigh Lake and the quality of low 5 class climbing/ scrambling on the CMC face, I think this is possibly the best and most logical "Picnic" in the Tetons.
Starting in downtown Jackson Hole, Wyoming under the antlers.
-Bike 25miles to Leigh Lake (water entrance at 43.798193, -110.727328)
-Swim ~2miles to the standard canoe drop off point for the CMC face of Mt. Moran (43.817544, -110.750168)
-Hike/Climb the CMC Face of Mt. Moran, 7miles and ~5700ft climbing and hiking (https://www.mountainproject.com/route/105823529/cmc-route)
-Swim ~2miles back to where you stashed the bikes
-Bike 25miles back to downtown Jackson