This route would probably take a day off route, as opposed to going all the way to Whitefish and then back into the park.
Anyone wanting to try this might consider calling the ranger station again for a second opinion on Outside versus Inside. Either way, you end up at the south end of McDonald Lake, the start of the Going to the Sun. The two campgrounds closest to the pass are Sprague Creek and Avalanche Creek, but I think he said the last place for food was at the Apgar Visitor center. From one of the campgrounds, you could go up to the pass and back down. The distance from the breakoff to Polebridge, to Apgar visitor center and the top of Logan Pass, then backtracking and moving on to Whitefish is about 118 miles. The straight GDMBR from the same breakoff directly to Whitefish is 49 miles and of course Logan Pass is all up, but not steep. If I interpret this document correctly, the grade does not exceed 6%.