Well, as far as new job goes: you can ask them if they're OK moving date, and explain why you want to move it. If they don't want to move date then they can't

Well, as far as new job goes: you can ask them if they're OK moving date, and explain why you want to move it. If they don't want to move date then they can't blame you for not staying on to see things go live, since they made the decision. And if it ever comes up in interview for future job (which is unlikely) you can explain it wasn't your choice. So: ask new employer to change date. If they're not OK just start new job as scheduled, it really doesn't seem like it's your fault since you did your best. And given that "business dramatically added scope and was changing requirements and demanding devs work nights/weekends to accommodate" if anyone is at fault, really, it's management at old company.