Three Sirius radio satellites which use this orbit were put into space using a heavy lift vehicle from the Soviets capable of putting 6 tons into GTO,
This makes me think that they are certainly beyond the LEO clutter. But given it took a 4 stage rocket to put them in place
http://en.wikipedia.org/wiki/Proton_%28rocket%29
it would be a serious challenge to put them into space after the war.
However from playing
Kerbal Space Program I do know that reducing the mass of the final product (in this case the satellite) significantly, would have an even greater effect on the amount of thrust required to reach the same orbit. If advanced Morrow technology could cut the weight in half and only one satellite per launch , perhaps a 2 stage system with only a small fraction of the Proton's thrust could pull it off.
Kerbal is not a perfect model of the earth, but it might help me refine those numbers.
edit
here is a video of a tundra orbit in Kerbal
https://www.youtube.com/watch?v=m-7ex5c-MRY
It seems to be similar to the height of a GTO
edit 2
confirmed
this shows the two orbits Molniya and Tundra
https://www.youtube.com/watch?v=kIA34oXiTC0#t=18m40s
if you stick with it for a few minutes it really shows how the 3 satellites work on unison to keep constant coverage over the US.