Big A Mountain in western Virginia is shorthand for "Big Ass" Mountain - -
Anyone who has climbed it on the TransAm knows what a killer it is.
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About your route and timing -
First, start on the coast - you'll be glad you did.
Second, six weeks should do you from coastal GA/SC to Pueblo.
So, I wouldn't leave any earlier than late April.
Third, the peak of storm season in the Great Plains is late May/early June.
It is always wise when cycling in Kansas to remember Dorothy's travails.
Fourth, we had some nice snow and cold this weekend in the Bighorn Mountains.
I lived in Jackson when it snowed on the 4th of July - a few inches, not flurries.
June can be fickle in the Rockies - often there is a late cold rain/warm snow system.
Some park and forest facilities do not open until mid/late June.
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Starting about April 23rd -
One week to Chattanooga, one more week to Cave-in-Rock,
one week to Pittsburg, KS, two weeks across Kansas and eastern Colorado.
That gets you to Pueblo at the end of May WITH an Atlantic coast start.
You might even want to wait until May 1st to start.
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If you haven't done much touring, I'd do the TA rather then the WX for sure.