I don’t think it’s the throwout bearing because you would’t be able to shift into any gear correctly if it was and there would be considerable slippage, nor do I think you need a new gearbox. If you did, again, you wouldn’t be able to shift most of the time and, if you did shift, you’d only have one or two gears, at most.
If your problem was the flywheel or the clutch plate then your transmission would be slipping like crazy, if you were able to get it into gear in the first place. And, if it were the linkages your Fiesta wouldn’t get into gear at all. The same is true with linkages and the rest.
What I think is happening is something that you haven’t mentioned. Normally, when you shift a dog collar slides forward to provide the initial linkage between shift. If the dogs don’t seat correctly (it’s just a place with gear cutouts), then you will find that your Fiesta will hop out of gear and that you may have to hold the shifter as you work through the gears.
Given the fact that your Fiesta is a decade old, I would suggest you swap out the transmission for a new one, if you can afford it. As you correctly noted there are lots of potential problems that can crop up when you work on a transmission. And, even though I am pretty certain of the cause of your Fiesta’s problem, you do have to realize that even if you fixed that problem, you might be introducing other problems due to the fix (other parts change and may weaken in situations like this, leading to continuing problems). So, rather than taking that chance, it’s best to cut bait and let things go by replacing the transmission entirely. You’ll have fewer headaches, in the long run. Of course, the cost will be in the $2,400 range, but, that’s not bad, all things considered, especially if you try to chase down and fix recurring individual problems.