Well now, THAT was an interesting discussion.
So in addition to reaching out to here, I reached out to The Gurus themselves. The folks at SAE (now SAE-ATI) Customer support. John Baloff pointed me to some documents posted on HiFi Engine, one of them was a "SAE Important Notice" document. Opened it up and it turns out that the instruction used in the SAE manual was incorrect. The manual said to insert the SAE in the Preamp out->Main Amp loop or the usual tape loop. Well, the Important Notice said "DO NOT PLACE THE 5000 between the preamp and the amp!"
In a nutshell, it needs a certain voltage level to work. the preamp->amp is a line level voltage that will drive the 5000 over the limit and cause the distortion I was hearing. So, move the SAE to tape 1 on my preamp, reroute the main signal into my DBX and so on.
I just finished an hours worth of testing and validation with a recording I know has pops/clicks/dirt that doesnt want to get cleaned. Sure enough, the distortion at the extreme ends of the sensitivity control is now gone. Only some residual humming (which is to be expected, according to SAE). The final test was to play a tape, while playing said poppy record and select the 'Tape Monitor' on the SAE and see which signal source was played. Sure enough, it was the tape! Change the input back to the turntable and playback from the turntable resumed.
All of these things are indeed fun (and enlightening), but damn - I swear there is a lot of black magic involved!