I think it's completely plausible that the Franz and the ASG Labs would have snagged the Heart, but Parasoul's SGM story seems to imply (at least to me) that Nancy was coerced into wishing on the Skull Heart by Double under the impression that Double or the Goddesses would intervene with the war. So my assumption would be that Double had reacquired the Heart at some point and passed it along to Nancy (which is what she would have had to do with or without it being destroyed along with Selene).
Some of the Labs' higher-ups (like Brain Drain) would definitely want to get the Skull Heart. At least, it feels like that, based on Robo-Fortune's story and some deleted endings.
Logically, it makes a lot of sense, considering that Lab 0 was researching Skullgirl blood.
Nancy was manipulated by Double, it's all but outright stated. She probably was chosen as a very good candidate.
Annie not destroying the Heart would be my biggest issue with my theory. She would never let it be allowed to get lost or taken by someone.
We need some official information on this.
I wouldn't believe she still could be on good terms with Big Band after something like that.
The obvious question to ask then would be if the Skull Heart can instantly respawn and revive the last Skullgirl, then why doesn't it always do that?
I thought it was a sort of an emergency respawn, because there wasn't any other candidate available. The Skull Heart usually has a lot of "human material", and Double seems to have a hand in choosing the best possible candidate. But this time the situation was completely different, and they had to use what they had. Marie wasn't even the "suitable" one, but there were no other opportunities in sight.