First, I'd suggest toughing it out in the short term. Directly disobeying an order that doesn't present an immediate life or limb concern will likely get you successfully fired.
You were not clear what this new policy is or how it came about? Did they cut the "floaters" and decide to use overtime to cover? Does your contract have a minimum manning clause requiring these slots be filled?
Has the Union consideed filing grievances each time this happens outside what your contract has outlined?
Lastly, would your union rather have station closures? If it came down to not being able to meet minimum apparatus manning, could they close a house and move personnel? While this is not a good situation, it might be the practical solution to not having enough personnel to cover minimum manning vs. tossing the minimum manning clause.
The suggestion to check your labor agreement (if there is one) for staffing regulation(s) is a good one. Your answer might be there.
Be careful what you ask for. Overtime is over pay (more pay) – an opportunity to make more than your salary. The goal is to create a balance. Ability to staff positions when needed but not to force so much overtime that morale and safety are compromised.
Also, your bargaining group may be able to use the amount of mandatory overtime to justify hiring more personnel.
At my department we have what you call "forced overtime", we call it mandated overtime. To keep minimum staffing, overtime to fill the vacancies is paged out to all of the department members. If the vacancies cannot be filled, members from the off going shift are "mandated" to stay. The mandated time is from 0800-2000hrs. The firefighter being mandated is paid at an overtime rate. The lowest ranking man on shift is mandated to stay. Once you have been mandated once in a fiscal year you are no longer eligible to be mandated and they work up the list of senority. Hope this helps.