Tire size?

That is correct. It might not be as bad on your truck since car haulers are in the range of 12k to 14k on the steer axle loaded.
With you running local it would probably work. 275/70.22.5 are mostly found in 18 ply (load range H) which has a weight rating at just over 7000 lbs per tire.
You won't get as much drop as you think using the 275/70's though.
The 295/65/22.5 that was mentioned is supposed to be mounted on a 9 inch wide wheel from what I remember.
KW's are too tall for car haulers so I doubt you will find any with the axles under them. There has been a few KW's over the years but not many.
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Google E-1322I. That's the 13,200" Spicer, which is the lightest rating having the 5" drop is available on their steer axles.