After spending an hour trying to troubleshoot, and after spraying cleaner on the contacts and POTS, I didn't see any improvement.
Since I've had the Combatstick 568 since 2004 or so, I'm not disappointed or upset. It probably had thousands and thousands of hours on it over a decade's time, so I suppose it shouldn't be of any surprise that components were starting to fail... especially when it comes to a device with moving parts and multiple potentiometers.
Long story short, even though I truly believe I was having similar issues to other owners of the Combatstick, I got my money's worth and upgraded to a new CH Fighterstick... I should be back in action tomorrow or Friday.
Thanks.