So no, you won't get across the Rockies in a month if you break the route up into equal thirds.
To get "over the Rockies" you need to get in about 2000 miles from Astoria. Suppose you shoot for Pueblo, a large enough town to stop and get transportation out. Pueblo is 2065.5 miles from Astoria. To do that in 30 days would require 69 miles a day, riding every day (plus perhaps 5-10% more for side trips and detours). That's still doable if you keep your load reasonable and start out in good shape. If you take a day off here or there (especially in Yellowstone), you'll need to average a bit more on your riding days.
Note that if you have three one-month segments to do this trip, you don't really need to get "over the Rockies" in the first month. You could just get through Yellowstone and Grand Teton and arrange transportation home from Jackson WY. That's what I'd suggest. But perhaps your second month will need to be in some month with weather not suitable for crossing the Rockies???
P.S. I'm confused by your words "over the Rockies into Colorado". Once you get "into Colorado", most of the Rockies are still in front of you.