For the benefit of any future forum/Google searchers, I'm fairly certaint that the process sending data to the Agilent power supply was the Tektronix VISA Resource Manager (TekVisaRM.exe). When I shut it off seemed to be the moment where the errors stopped going to the power supply.
I disabled it from starting up on boot and have yet to hear the error beeps. Time will tell if the Keithleys improve as well, I can't make them crash on demand.