There are a few methods I believe, and you should test them on small samples...
What kind of quantities are we talking? And do you mean all SolidWorks file types, or just .sldprt? Also it depends on how your variables are mapped. If you map from model to drawing and the drawing data cards are blank that is more of a pain (that was our situation).
1) SolidWorks Task Scheduler: you have to check-out the files to update, run the Convert Task, and check-in. If they were in a Released state then the revision stamp is broken (as far as the PDM database is concerned), so you would need a special workflow transition if you want to re-release. This will work for slddrw, even if they get properties from the model.
2) Open the files manually and save them in SolidWorks. Check-in. If your variable mapping is set up it should fill in the data card.
3) EPDM File Version Upgrade Tool (you have it, but it is not installed by default). Install it from some location like this: C:\swdist\pdmwenterprise\Support\File Version Upgrade\File Version Upgrade.exe
Then step thru the wizard. This is pretty cool, with some limitations. It will automatically check-out files, rebuild them and check-in. If they are Released Revisions it will maintain that. When it opens SolidWorks it does not launch the EPDM add-in, so you will need to test if it fills in the datacards for you. Without the Add-in it does not work if the .slddrw files have their properties mapped from the model, then it won't fill in the drawing data cards. I don't know what it will do with sldprt and sldasm, but I suspect it will work. If you start with a session of SolidWorks up (with the add-in) it will use that session, but mine always crashed after a few dozen files, and then it reopens SW without the add-in for the rest of the work.
Thanks Brian for the response and the info. The Version Upgrade Tool is a good tool to know about. Follow up for your info, I had a few part files with maybe 20-40 configurations. I got the few I needed fixed by removing them from pdm and putting them back. I have at least a dozen more and will be correcting these with the version upgrade.