For anyone trying to end the main game friendly with the Brotherhood, Minutemen, and Railroad, this is how I did it. This series of events gave me what I think was the maximum amount of lore-friendly main quest gameplay (having done missions for all 4 factions) and developed my character in a particularly unique way, as a sort of peacekeeper and unifier.

1. Join the Brotherhood
2. Brotherhood quests until Blind Betrayal
3. Complete Blind Betrayal whichever way you want (as long as you stay friendly with BoS)
4. Have an existential crisis and join the Railroad
5. Railroad quests until the Battle of Bunker Hill
6. Free the synths in Bunker Hill (as per the Railroad questline)
7. Confront Father in the CIT ruins and tell him you're leaving the Institute
8. Return to Desdemona and tell her you've been kicked out of the Institute
9. She will send you to the Minutemen
10. Minutemen quests until completion (destroy the Institute with them)
11. (Optional) Download this mod and get the Brotherhood ending reward in a lore-friendly way (it is restored cut content)

Regrets:

-Destroying the Institute too soon led me to regret not letting it hang around for a while for its traders/radiant quest/interesting scenery now that I've got pretty much nothing left to do

-I really wish I had gotten to see Liberty Prime in action