It's difficult to see the radiator in accords, but do this, as it is relatively easy: loosen the bottom bolt and remove the top two in the condenser fan motor assembly (the one on the right as you face the engine working). This gives you a better view of the radiator. Often Accord radiators will start to oxidize horribly- it would be apparent with a visual inspection. The fins turn into the consistency of dry leaves and flake out when you run your finger or a screwdriver across them. If the fins are that bad, the actual coolant passages in the radiator are not far behind. You begin to suffer from significantly reduced cooling ability because the fins are no longer dissipating heat at the same rate, and the actual passages inside the radiator can become clogged as the radiator releases debris internally as it breaks down, and the passages in the radiator are also the most narrow in the entire system- meaning if there is junk in there, that's where it gets stuck, again reducing cooling efficiency.
If you are running AC all of the time, I personally had an Accord that would only overheat at idle with the AC on- turned out it was simply the heat of the condenser actually contributing so much heat that the car would overheat at idle. Then of course while driving the condenser did its job and cooled the freon, eliminating the problem. I mentioned the radiator fan for that reason, it would create that same "idle only" overheating issue. As I mentioned before the radiator timer control unit is located behind the glovebox and I would not rule out that it could be failing.
In a nutshell, here is the exhaustive list of all possible culprits with those particular symptoms, and you can of course rule out what you have already checked:
-Radiator Fan
-AC Condenser Fan (only if problem occurs exclusively at idle with AC on)
-Radiator reduced flow/extreme erosion of fins
-Radiator Fan Timer Unit
-Radiator fan wiring (perhaps damaged and repaired in an accident at some time? Occasionally you'll find front end wiring harness components have been spliced thanks to an accident)
-Thermostat (Only if thermostat were faulty and somehow the increased pressure of higher RPM's was forcing it open while driving, but at idle there was insufficient pressure being generated by the pump to compensate for a thermostat that is too stiff)
The last few are definitely highly unlikely, but take all that for what it's worth. Good luck and keep us posted. Oh and as for bleeding, for what it's worth, I have always had the best luck squeezing the upper and lower hoses frequently as I add coolant, and running the car then adding more and repeating that a few times if you are really trying to be sure. I have never had a pocket that I know of after just filling once, then filling again after running it for a few moments.