Welcome to the ACA's forums!
I would say that your plan is a bit ambitious as to the timing. My guess is that if you ride the Northern Tier west of the Rockies, some or all of the major passes may still be snowed in, especially since you are cranking out 100 mile days. If Colorado can be iffy on the weather, think about what Idaho and Wyoming will be like in May. Once you get east of the Rockies, you are good to go (but cool perhaps). Also, the Going-to-the-Sun Road will most likely still be closed.
However, if you are riding the TransAm to Missoula then connecting to the Northern Tier route via a section of the Lewis & Clark route, it "probably" is doable. Worst case is you have a day or two holed up in a hotel and wait out a late season snow storm. If you choose to do the TransAm to Yellowstone then switch to the Peaks, Parks, and Prairie route, you definitely may have some issues in Yellowstone and in the Big Horn Mountains west of Buffalo, WY.
How much time do you have? Have you considered riding the Pacific Coast up to the route of your choice then heading east. This would give you one to two more weeks for things to thaw out some. If you do this, please note that you will most likely have headwinds everyday along the coast (at least until Oregon). I did the S>N ride in my early 20s and it was doable but I definitely had a harder time than those coasting with the wind southbound.
Another thing to consider is that due to the early season, don't be surprise if hotels are not open until Memorial Day weekend so you definitely want to plan your stops 3-4 days in advance (call them) in case you have to take some shorter days or plan a longer one.
Finally, you will definitely want to take some decent rain gear that WILL keep you dry. Being wet and cold is not a good combination.
Whatever route you choose, I would encourage you to check out WeatherSpark.com and review the historical climate data for the route(s) you are considering. Remember these are averages so the temps can easily be off by 10*.
Have a great ride (and run, but we won't talk about "runners"
). Tailwinds, John