I know this is an old post, but I have a problem with drift on channel 1 of my E3646A, but it seems different than what you described. I really want to figure out how to repair and troubleshoot this issue!
Mine will slowly drift down, until it hits a certain threshold, and then jump back up to the set voltage (or close to it). See video above (and sorry about the noisy kids in the background). Only happens on channel 1, so i don't use that one anymore. Bought it off ebay for $160-ish (a steal!), and after finding this issue, the seller offered are partial or full refund (so i asked for $100 refund if I could keep it).