The answer depends on whether you're willing to play hardball while you still have some negotiating leverage. If you are, your first step is to make sure you and the other two members of your team keep accurate records of where your time is going for the next month -- exactly what tasks you work on and how much effort each required for completion. You'll need this as ammunition.
When you have the data, ask for a meeting that includes your three-person team (or just you if they chicken out), your manager, your manager's manager, and the integrator project manager. Lay out everything you were given to do over the past month and, using your time-tracking data, demonstrate how many hours of effort would have been needed to get them all done (presumably, enough work for at least six full-time employees, but let the data speak for itself).
At this point your management will let you know that "this isn't a 40-hour-a-week job, you know" (if you're exempt) or "we pay you for your overtime, you know" (if you aren't). Turn to the integrator project manager and ask, "Speaking as a professional project manager, what happens to quality when people work those kind of hours?"
If the project manager has even a shred of integrity, you'll get the answer you need.
That's when you say to your manager, "We need the two of you to run interference for us so that we can do our part to help this project be successful. We need you to say no to as many business requests as possible, to give us time to work on the conversion, because otherwise we have no chance."
If your manager weasels, you turn to his/her manager and say, "It appears our manager doesn't have the authority to say no. Can you help make this work? Because otherwise we'll be the ones making the decisions, and that's going to make all of us look bad."
Assume you get over this hump and everyone agrees to a governance process that cuts your task load to a semi-manageable level. That's when you say, "We have one more topic. It's the elephant in the room, and it's time we all acknowledge it's there. The elephant is our future in this organization once the conversion is complete. Do we have one?"
After your manager's manager finishes the traditional polite hand-waving, say, "What you're saying sounds terrific. Can we put something solid behind it? Because as things stand, no matter what you say about loyalty and gratitude for hard work, when we turn off the old system, the three of us will have none of the skills you need us to have to be productive members of the organization. You're asking us to work long, hard hours. That's fine -- now what will you do for us so we're part of the new system team when we turn it on?"