Approvals: How to automatically re-assign task after due date?

However, this has led to delays, so we’d like to implement an override feature:

If both parties haven't responded within 24 hours, one admin should be able to override and initiate next steps of the process. 

Hi Hazel,

Sure, if both parties haven't responded within 24 hours, you can escalate the task to another person to override and initiate the next steps of the process, let me show you how:

1. In Workflow Builder, click on the Gear icon beside the Approval element.
2. On the right panel that opens up, click the Advanced tab.
3. Toggle Escalation to ON position, and then set up Due Date for Escalation.
4. Enter the new approver's email address under the Escalate Task section.

This setup will help reduce delays by ensuring the process moves forward by escalating the task to a new assignee after the due date.  You can check out this guide about How to Set Up Approval in Jotform Workflows for more information.

Give it a try and let us know how it goes.