I don't know if I can help much on this as I've never seen this particular problem, but something did come to mind. Your idle controls seem to be working because you do get your high idle when a bit cooler. The fuel mixture changes in relation to engine temp (especially at start up) so that may be related. I've seen some things related to engine deposits that may help.
As mileage builds up on an engine, deposits can build up (hence all the oil co.'s telling us their gas is cleaner).This will happen with any fuel though. The intake valves are especially prone to this because the fuel in the intake at shutdown kind of burns or evaporates off the backs of the valves and leaves a residue or carbon that accumulates over time. On cold start, these deposits tend to sort of soak up the fuel until they are saturated. The fuel mixture is richer the cooler the starting temp is and this could account for the difference. I have personally seen a couple of vehicles where the deposits were so bad it would intermittantly cause the valves to stick. In my shop, we have seen many Factory TSB's related to this issue and cold start/run problems.
There are several options to try if you decide to:
1.Many shops and dealerships use a product called BG 44K. It goes in your tank. This is only sold to the repair market, but most will sell it over the counter. It will set you back $20-25, but this is a very strong product. It will clean the injectors as well.
BG products 2. The Techron products are good, but not near as strong. Multiple treatments or double doses would be needed.
3. The local Carquest sells a product called "Seafoam" (yes I know its a riduculous name and I avoided it for a long time for that reason, but it saved my butt once). This is one of those products like Marvel Mystery Oil which says it does it all. Anyway you can pull about half a can of this through the pcv line then let the motor sit for awhile before running the rest. The idea is that it soaks into the deposits. Be very careful not to go too fast, because it is possible to hydro-lock an engine doing this. I had a Dodge Avenger that another shop had diagnosed as a broken timing belt and it sure sounded like it. Faster than normal cranking speed / no start and low compression. Disassembly found no problems with the belt, and research turned up a TSB about deposits holding the valves open. After treating with the Seafoam and running another can thru our injection machine that dodge ran great.
4. Find a shop that uses the Carbon Clean system. A fuel system / fuel injection cleaning with the right chemicals will produce the fastest results, but cost the most.
Sorry for such a long post, and this is just a shot in the dark, but the situations I've seen related to this are real.
So maybe this is worth a shot. I've seen these products cure problems I didn't expect them to and many times after someone had already tried other fuel injection cleaners or treatments.
Hope this helps.
PS. Just saw a post about valve adjustment also. This is a very important maintenance on the 2.6 and can cause some weird problems and eventaully burn a valve. Another good area to consider.
Dave.
