We usually raise double crop soybeans..  No we do not have to report them separately.  However, USDA does track them.. like they track everything else.. I believe in a Crop Production report.. there's a line item buried in the report on the amount of double crop acres.. the double crop belt stretches across Ks, Mo, Southern Illinois, Kentucky.. to the Carolina's.. either side of  area..  We mostly do irrigated but to our east is a big dryland double crop area.. like.. 40 to 50% of the crop (or more.. or less.. depends on the year..)

We cut our irrigated wheat acres down.. hence we cut our double crop bean area down this year.. hence we raised more fuller season beans.. which as you implie should yield more..  However we had to spray them more 3 herbacide passes vs once with double crop.. and I actually think I can raise the double crop beans cheaper.. but they are more risky yield wise.. feast or famine.

I don't know if this answers everything but fwiw.

US Double crop Soybean acreage varies from about 5 to 10% of the whole crop.. so it's one of the variables.

This year.. Ks had a tremendous amount of growth in Dryland full season beans.. get the drought monitor out.. and look at the yellow area's.. that's where it mostly went.. but they'll have something.. 25.. 35.. 45 bu beans.. good.. but down from last year's 45..55..60 bu beans.. and as I've shown this year the dryland double crops to my east are looking pretty tough also.. but there's alot of em planted..  lower yields.. more acres.. so probably total production close to last year.. but I'd expect down a little.. but who knows?

On our farm your premise is spot on.. more beans on fewer acres.. because of less double cropping vs normal.