That makes sense, Researcher, doubles sure were outsold in that time period! I wonder if Remington lost money in the end buying Parker?

To quote The Parker Story (page 163), "it is clear that this (Remington's acquisition of Parker) was not a wise move from a financial standpoint."
Remington paid over $750,000 just for the right to make Parker guns. During the seven years of production they produced a little over 6200 guns. They were plagued by high production costs and a dwindling market for high-quality doubles.

I wonder if that 6,400 includes both Meriden and Ilion production?

According to The Parker Story, the total Remington production of Parker guns was 6,224: 4,629 in Meriden and 1,595 in Ilion.

Sales of luxury items, like Parker Bros. shotguns, tanked after late 1929. I find the transition covers guns in the 234xxx, 235xxx and 236xxx range. My 20-gauge VH 235178 was Made and shipped in the fall of 1930. I find some guns in the 234xxx range with the PARKER GUN WORKS OVERLOAD PROVED stamping and find guns in the very high 236xxx range with the PARKER BROS. OVERLOAD PROVED stamp, one of which does have an AD (A = March D = 1935) Remington date code?!?

The Parker Story states "the first gun placed in production under Remington management was 236531, a VH grade 28-gauge shotgun with 26-inch barrels. There were lower numbered guns, both finished and unfinished, in Parker Brothers inventory when Remington took over, but 236531 was the first serial number assigned under Remington management." The Remington Parkers chapter ends with "Remington produced a total of 6,224 Parker guns, 4,629 in Meriden and 1,595 in Ilion."

Are you familiar with the graded 1894's? The workmanship is outstanding and it could be argued the engraving is better i.e. no flying turnips.

No, I'm not. Except for one Remington BE grade 1894, my experience is limited to the 1900 K grades and 1894 A grades.
I was comparing my K grade Remingtons to my Parker Trojans and my A grade Remingtons to my VH Parkers. While the Remingtons were very good guns, I feel that the Parkers were built better in the lower grades. There was almost no engraving on those models, so there was nothing to compare in that respect.