what was considered mass production in the 30s and what was mass production in the 40s during the war years are two different things. RR may not have been working 8 hour days in the early 30s but they weren't working 24 hours a day either.
P & W was supposed to have built around 13,500 engines from 1925 to late 1938 and that included Wasps, Wasp Juniors, Hornet A's and Hornet B's (different bore and stroke), Twin Wasp Juniors, Twin Wasps and a few Twin Hornets.
Wright built about 8,000 Cyclones from when it was introduced (as the R-1750 ?) until Aug of 1938.
Rolls wasn't that far off when it came to aircraft engine production.