Have to give credit to my VAR, CADimensions, where a few folks there scoured the solutions database of SolidWorks relentlessly before we found the smoking gun.
Our setup is typical, where we have SolidNetWork License Manager distributing shared licenses to our users at multiple sites, so this may not be applicable for standalone SolidWorks installations with a fixed license.
Here's the fix --> Take a look inside C:\ProgramData\FLEXnet and delete everything inside there. When SolidWorks starts and grabs a license it creates a temporary file (.data) in there. The presence of the old Connect subfolder and the other files was the culprit.
Once deleted, SolidWorks startup times were reduced from ~27 seconds to 6-7 seconds. Not only that, but the slow performance with our PDM add-in turned on in SolidWorks also vanished. One assembly I used for bench marking was taking 1:33 (m:s) to open and after this fix now takes 8 seconds. The "lag" when toggling between open documents in SolidWorks is also gone. Somehow, someway, this license file/folder issue dramatically impacted SolidWorks performance. I've performed this fix on five of our computers here and have verified the same performance improvement for all. We are now actively pushing an update out via our Group Policy to delete this folder's contents for our remaining 100ish users.
Note, when deleting the folder contents, first make sure there is not a running session of SolidWorks. It keeps the .data file open and is write-protected when running.
I hope this works for many out there, I know for myself this was a great solution. Post your results/findings!