Dave, Parker used the word Quality with letters in their price lists and numbers along with barrel steel in the stock books. That's the criteria I use in research letters.

Your gun is of the highest conditions 0 grades seen in a long time. It's no 'rule of thumb' but the lower grades were often working guns who earned their keep.
I have one of the same configuration though not nearly so nice. It's a joy to shoot. However, I can't remember when I last shot a Parker that wasn't.

I just thumbed through my collection of Parker catalogs and see that they used the word Quality with the letter designations into the early 1920s. In the April 21, 1923, catalog the SBTs and the A1 Special and AAHE are preceded by the word Quality while the others are not. The page for restocking prices uses Quality for all of them. By the January 1, 1927, catalog the only use of the word Quality is on the SBT page where it states "Offered in five grades, corresponding in quality to our high grade double guns as shown below."

In the Jan. 1, 1929 & 1930 , catalogs it states "P.H. and P.H.E. Grades Discontinued." By the big Remington era catalog they are all Grades. So, as with many things, Grade and Quality just don't fit into a neat and tidy order.