I contacted Microsoft's mobile group on Facebook about this issue, and they suggested that I reinstall the cable driver. Tried that and...almost got it to connect. I got to thinking that if it's the cable driver that's not working right, maybe I should try to connect without a cable. I grabbed my little Bluetooth kernel and plugged it into my laptop and...SUCCESS!!! I was able to sync my day-to-day stuff (pics, contacts, text messages) with no problem. I tried to backup my phone with the suite and it went REALLY slowly, but it worked (I backed up my phone a week or so before updating to Win10, so I wasn't really too concerned about not finishing the backup today).
So, if you have a way to connect to your computer by Bluetooth, give it a try and it /should/ work to connect to Nokia Suite. I still want to resolve this issue with the cable connectivity, though, as much out of principle as it is out of convenience. Bugging the hell out of me...