Hi, RJay,
You are correct about the cartridge. I had forgotten all about that Remington cartridge, or rather that Remington name for the .22 WRF. The Remington Model 16 autoloader was chambered for .22 Short, .22 LR, and .22 Remington Special from 1914 to 1918. After that it was made only in the .22 Remington Auto round (not quite the same as the .22 Winchester Auto). The Model 121S pump action was also made for the .22 Remington Special in the same short period, but I don't know of any other rifles that were.
I don't have an H&R .22 Special revolver, but it was made well into the 1930's, by which time the .22 Remington Special was totally obsolete. Every reference I can find, plus the statements made here by others, is that it was chambered for both .22 LR and .22 WRF, and was marked the same for either cartridge. I can find no reference to the ".22 Remington Special" in H&R catalogs or in any other book in reference to that revolver. Barring further solid evidence, I will stand by the statement that the word "Special" applied to the gun, not to the .22 Remington Special cartridge or to any arrangement with Remington.
Jim