Department Change SLAs

Department Change SLAs

We have an issue where we change a department for a ticket. We have an SLA applied to all tickets for all departments (72 hours). However, when we move an item to a different department to original SLA is overwritten. I was looking into setting up a new SLA or Workflow rule to apply the original SLA but do not see any options in the rules for when a Department is changed.

Has anybody else ran into this and what workarounds did you have for this?