We've had our DMM6500 lock-up a few times over the past couple years, and recall it was something graphing related, but not enough times to be of concern or make note of.
Since you've indicated this only happens with the graphing function and everything else is fine, leads one to consider a hardware issue that becomes relevant only when the graphing is enabled which might point to some unique graphics memory or logic use. Having the issue over different firmware revisions also points to some graphics related hardware problem.
As you've discovered these Keithley DMMs (also the KS34465As) are in another class of DMM instruments and why we have both types!!
Anyway, hope you can get this graphing issue worked out, this is where the Keithley stands out
Best