Okay. I spoke with a mechanic friend (non-Ford) this weekend and found that the only thing that he could think of that could cause this problem is an open, or stuck, IAC valve. The theory is that if the engine was still cold when it was last turned off, the IAC valve would still open to keep the idle high. Then, the next time the car is started, the valve is either not told to close or is stuck open and would result in a difficult start to an incomplete choke. This theory sounded reasonable to me (particularly since another user in these groups seemed to have solved his problem when the dealer replaced the IAC valve -among other things). Does this explanation sound feasible to anyone? Either way, I'm going to attempt to find an aftermarket IAC valve (or perhaps an '05 *automatic* version) this week. I'll let you know how it goes.
P.s. Any thoughts would be more than welcome.