I feel very sorry for you. That's really poor management (I'm a manager of a team of 8)
Forget the specific issue. The wider issue is your two managers.
Don't do any work over the weekend. Do plan a conversation for Monday with them both, where you clearly set out your workload concerns and what you need.
Be very clear.
It's their job to manage this situation.
If they don't listen or are not positive, you need to escalate it.
In the meantime, decide the remit of your job and only do that. Keep emailing updates on your situation. If they raise issues about work completion, refer them to the emails.
If nothing improves, it's time to leave.
About the particular situation, I'd cc in your manager in future and leave it at that (after chasing twice). I wouldn't continue to follow up and I wouldn't ask them to step in.
Try not to think too much about it over the weekend 💐