All of this is an argument not to have Fortune in the Middle type effects in your game. This is a perfectly valid preference. There aren't a huge amount of them in 5e, and I imagine they can all be removed or altered fairly easily.
However, as printed, 2014 5e (and I assume 2024 5e) does include them. They are there. If you keep them in and use them, a Fortune in the Middle approach allows them to be used without doing the fiction-bending shenanigans you describe.
I'm not aware that 5e really addresses this one way or another, so I don't believe your comments about 'once a roll is made, that's it' are supported by the text. Given feats like Lucky, the strong implication is in fact that 'once a dice roll is made, that's not necessarily it'.