For some reason the post game loading screens are stuck loading infinitely so I can't actually test anything, but there is a setting you can try.
Map > Game Variants > Player Attributes > Hidden Attributes > Color
This prevents players from having the option from selecting their color in the lobby and it MIGHT remove color form showing in the post game screen, but again I can't actually test myself. If that does happen to work you could mess around with Score Results or Score Values in the Advanced Game Data section of the data editor to try and show country name is the post game screen. Other than that I don't see much else that can be done in the way of your two ideas.
An entirely different solution that I know works is just making your own score screen that shows in game before players leave, then not showing the default one at all. It is more work to set up but allows for even more customization.
For some reason the post game loading screens are stuck loading infinitely so I can't actually test anything, but there is a setting you can try.
Map > Game Variants > Player Attributes > Hidden Attributes > Color
This prevents players from having the option from selecting their color in the lobby and it MIGHT remove color form showing in the post game screen, but again I can't actually test myself. If that does happen to work you could mess around with Score Results or Score Values in the Advanced Game Data section of the data editor to try and show country name is the post game screen. Other than that I don't see much else that can be done in the way of your two ideas.
An entirely different solution that I know works is just making your own score screen that shows in game before players leave, then not showing the default one at all. It is more work to set up but allows for even more customization.