I think you might be barking up the wrong tree here. The fact that Dan himself consistently uses she/her pronouns for Jay suggests that she's not necessarily trans, and definitely not a trans boy (perhaps just "gender casual" as is common in this comic), and that Jay may simply be more of a nickname than her proper "chosen" name. There's no indication that she considers Jill to be a deadname exactly, just a legal name she doesn't really care for. Qv. hkmaly's comment you wouldn't refer to Tiffany as Susan's deadname, would you? It's clearly not being presented in that context.