It will fit.You don't sound concerned with absolute originality,so it won't be a problem.You will have to shim up the radiator a little,as the 30-31 has depressed pads in the crossmember for the high radiator,and the 28-29 had raised pads.Not a big deal.
...and here, the factory did that, including the shims, on early 1930 pickups that retained the '29 type body for a while.
The parts book carried the late version of frame as the direct replacement for '29's, too.