However on channel 2 when set exactly the same the DP832A display shows 0.005A at only 8.765 vdc. I confirmed with the Agilent meter that the actual current was only 4.375 ma @ 8.750vdc and I have to increase the current to 0.006 to reach 10.000v.
If I understand this correctly you had it in cc mode to the last digit and found it to be 1 mA out? The extra resolution does not translate to accuracy, so are there published specs for the DP832A? Both channels may be in spec, even if channel one performs better.
I just tried this on a regular DP832 with a 3.3 KOhm resistor (unmeasured) and got 0.005 A on channel 1 and 0.006 A on channel 2 at 10V, so obviously not very accurate, but the may be in spec. Perhaps might improve a bit if left on.
As for your other issue, sounds like a firmware bug.
[EDIT], after leaving on for a bit Channel 2 went to 5 mA, still not right but better than before.
[EDIT AGAIN], now its down to 4 mA on channel 2, so perhaps leave it run for a bit.