This mod will allow you to solve the issue of Danse's identity and has several other new options that weren't included in the original game.

You will be able to choose between two main options: help Danse decide what to do, or suggest that he should leave the Commonwealth and make a fresh start. The first option will take you to the vanilla path, with one change: after the confrontation with Maxson, if you repeat he should leave before Maxson changes his mind, Danse will actually go and LEAVE the Commonwealth.

The other option is to return to the Brotherhood will lead you to a new quest during which the duel takes place and a new Elder is decided (if you refuse to execute Danse when confronted by Maxson of course). This will give you an extra option during the Tactical Thinking quest but is not expanded upon any further.

If you have already beaten the main quest with either the Brotherhood or the Minutemen; you can talk to Danse while he is not your companion to get a new dialogue option (medium repeatable speech check) that will trigger the duel quest.