Your missing some cool places with that itinerary but you can't see it all. Why Monument Valley? I prefer Canyon DeChelly (pronounced Dee-Shay). Met a code-talker there once who explained how he was made to remain "silent" on what he'd done for 20 years, mostly treated like 2nd class citizen since...
Flag is a good base, mountain town, still cold then but several outstanding day trips possible in any direction, even G.C. park (a long day though). Closer yet is Williams where you can take the train to G.C. village, get off for a while, and back (for tourists --sorry but I think that's you). Closer yet is Tusayan, just outside the parks entrance. Average time/visitor at south rim is like 2 hours... most are heading to Vegas. A shame to travel all that way to look down and say Wow. It's probably too late to get a room within the park but it would be worth it, especially El Tovar; Maswick a close second. If you have just one point to visit... it would probably be Desert View and you could do that coming down of 89 as it is the east end.