My son and I did a western trip several years ago (after school had started) and had a ball. Traffic was light and the animals were out and about eating everything in site. Only problem we had was our plan called for heading out across the Beartooth and into Montana at RedLodge to I-90. Had a heavy snow our last night there and the pass got closed. We had to go back across the park and exit up through the west entrance.
Said all that to say this - late is better, but too late is not as much fun