Route 66 is way far south of the parks you mention (Yellowstone, Tetons, Glacier). On the other hand, those parks closer to 66 (Grand Canyon comes to mind, perhaps Zion, Bryce, Death Valley) will be hot in the summer. For 4-6 weeks from Florida, that's a lot of territory, IMO. Do-able, yes, but you say you will be taking it easy and going slower than many do - in which case you may not have enough time to do justice to all of those parks. I'd cut one of them out - again, just my 2 cents. It's a big country. :)
An alternative: do just some of the 66 that's available (and there isn't a lot of it), don't go all the way to California, but head north once you get to NM or so. Lots of pretty scenery from there thru Colorado, Utah & Idaho on the way up to the Tetons.