Car, continued

So, the mechanic explained what's going on. Firstly, the problem is intermittent. Intermittent problems are always the hardest to track down as conditions have to be Just Right for the problem to occur, and it can take just the right amount of Good Fortune to figure out which conditions are affecting the issue. Even then, not all of those conditions may be under your control. Next, they were reasonably sure they had tracked down the problem to malfunctioning electronics relating to the fuel supply, but when they called Ford to get a quote for the replacement part, Ford said "No, that part never ever fails, couldn't possibly be that part, your diagnosis must be wrong".

However, in their investigations, the shop discovered there is a recall on the fuel pump for my car. This may or may not fix the problem, but we can at least get it replaced for free to eliminate it from the issues. So the car is currently with a Ford dealer, as they take care of that.