The positional justification of the Scandinavian is that Nc3 blocks the c pawn. In addition, your Bc8 is locked. So don't play 3...Qxd5. You won't get anything close to the Scandinavian.
You better bite the bullet and play 3...exd5. For inspiration, look what strong GMs are doing to get a good game. I remember to have some nice games of Mikhail Gurevich but any other strong French player will have some antidote for the Exchange Var as well.
Using a very outdated windows vist computer right now so the diagram once againn wont work. 1.e4/e6 2.d4/d5 3.exd5/Qxd5 I play this cause I hate going into the boring/drawish regular exchange lines. 4.c4 if white plays anything else it usually just ends up in Scandinavian lines which I dont mind. 4...Qd8 5.Nc3/Nf6 6.Nf3/c6 7.Bd3/Nbd7 8.Bf4.