Mine pulls to the right like that too, it also pulls to the left when the road is sloped to the left. I think that may have more to do with the crown in the road than anything else. Your shimmy or shake sounds like a balance problem to me or possibly a tire that has a small lump.

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1985 300D Turbo ~225k
2000 F350 (Powerstroke) 4X4, SWB, CC, SRW, 6spd ~148k
1999 International 4900, DT466e (250hp/660 ft/lbs), Allison MD3060 ~73k