Like I said, in my experience, calling the spec to be 1/2" processed instead of 3/4" natural, it was actually cheaper to get the 1/2" processed then to run continuous sieves until a suitable natural material was discovered (One time it took in excess of a dozen sieves to be performed before the material was accepted).
Dry sieve vs. washed sieve is really an opinion stance. Certain engineers like the washed sieve so they can determine the actual amount of fines in the material, but an added bonus is that it provides a "cleaner" sieve of the material (and just may knock your 3/4" retained to under 30%). I would recommend reading up on ASTM D422 for washed sieves.
As an added note, you may just be able to argue your case to use D1557 yet. If you read section 5.3.1 of D1557 closely, it says "soils containing more than 30% oversize fraction...are a problem." So if you're right at 30.00%, you could try to argue that you can use D1557 to determine your proctor.
Finally, you could try D4914 or D5030, which could determine "field" dry unit weights. However, the downside to these two methods are they're not widely used and they're rather costly.