Okay, further experimenting today has yielded the following ...
1. Dos Mos > Big D > CPR = POO. Really, terrible tone; it's contricted and flatulent.
2. Dos Mos > CPR > Big D = GODLY !!! The tone is smooth, very pro sounding, and postiviely HUGE!! It's like all the detail that gets captured by the Dos Mos is then enlarged and made beefier before it goes to the OD. I'm also not experiencing that diminishing of the pick attack any more!
I can see that I'm going to have a lot of fun with this pedal.