In short, in the next HD version, it will be possible to navigate through folders in the scenario manager.
In this regard, it is possible to change the way saves are stored. Make it so that saves for one game are written to their own folder.

And here is the question: how exactly should this be implemented (I would like a single, optimal solution, without any unnecessary settings)?

Here are some different options:

1: [Random map name]\112.gm2 (The random map name currently looks like Player1 vs Player2 (3))
2: HotA[Random map name]\112.gm2
SoD[Random map name]\112.gm2
3: Player1 vs Player2\3\112.gm2
or maybe
4: Player1 vs Player2\2SM2c, M+U, 1441608083\112.gm2

Or some other similar mixed option based on these three.

How should it be done?