Mid-June is early in the Northern Rockies.
Especially in a big-winter year - which this year is turning out to be.
And for a gamecock from the land of palmettos swaying in the breeze.
If you are departing from Mammoth Cave on April 30-
that would put you in Pueblo in late May.
If you are departing from Yorktown - more like mid June.
A late May to mid June transit from Pueblo to Missoula could be challenging.
If you want to connect with the Northern Tier from Missoula may I suggest:
Hwy 200 to Thompson Falls
Thompson Pass Road to Cataldo
Trail of the Coeur d'Alenes to Plummer
(Paved with lakeside camping in Harrison - spectacular)
Paved county road via Fairfield & Spangle to Cheney
(Skipping Spokane - unless you really want to hit the city)
Thru Medical Lake to Deep Creek and US 2
Excellent stretches of Old Sunset Highway to Davenport
Then continue on US 2 to Grand Coulee Dam.
(Make sure to cut down to Steamboat to see the stunning Grand Coulee)
Hwy 174, Hwy 17, Hwy 173 to Brewster
Then US 97 and Hwy 153 to Twisp and Northern Tier
(Excellent paved back roads in Methow Valley)
Can't say for sure what the weather will be -
But if you are riding the Rockies in late spring, you will welcome sun and warmth.
The stretch from Deep Creek to Pateros is on the Columbia Plateau.
If you head straight to the Northern Tier from Missoula you will not get much warmth.
June Averages -
Republic - 74/43; Grand Coulee - 79/53
I live in Wyoming -
I have frequently gone x-c skiing on fresh snow in early June.
I have ridden every county in Washington and know the roads pretty well.
Same goes for N. Idaho and W. Montana.
If you are interested, I'll give you more detailed info.
Trail of the CdA:
Trail of the Coeur d'Alenes bike path in the Idaho Panhandle
Old Sunset Highway: