Not sure what Black was doing playing 2...e5 that seemed weak.
The problem with the BDG when playing against the Center Counter.. IMo it revolves around playing 5...c6 (and controlling the surrounding squares) and playing the Bishop to f5 or g4 .... if successful, the BDG seems to fizzle out (plus shutdown any attacks on on f7 and Black is fine.)
Some examples (not my analysis... Years ago... when I played competitively I played these lines and got a few good games.)
Maybe use these.. to come up with some ideas to counter the 5..c6
Hope this helps
I sometimes like to try and transpose into a Blackmar gambit or a KG when facing the Scandinavian. This guy sprang this funny move on me (3...Bb4+ in my games) and then a piece sac, and it led to some real crazy stuff. I got clobbered in the first game, but bounced back in the second.
Here's a game with Hungarian GM Tamas Banusz playing the black side with the more usual move order, a KGD. The notes are from lichess.
And here's my games. I'm a basement level player, so expect a lot of blunders!
And the rematch.....