Imo you just tried too hard to oorp change everything overnight and control all diplomacy.
You can easily build on what past BD have done and slowly change it over many months through subtle story development and in game interactions without throwing history under the bus or trying to do 180s right away.
GC fix is easy. Just accept the "-.5" or whatever rep is there of mutual distrust,there's no need to fight it or try retconning it. And fix it over time by the simple routine of
1) Log
2) Find GC
3) Do good stuff together like helping them with KNF and in game RP
4) do RP post based on interactions
And slowly you move from -.5 to +.5 or whatever can be there given that BD are anti-cardie but their main goals are more important, inch by inch, based on every interaction. You will have setbacks(siege oopsie) But that's part of the game.
Same with coalition. You can oorp think what makes sense, but you should do progression and logically build on RP.
And lastly - BD and GC are not one and the same. You are allowed to have different allies, RP and goals. You don't need to control them, you don't need to be max green to help and supply each other against the Government
