The problem here is the PM does not see himself a part of the team, your team, but is on 'other' team that is driven by other gears. The estimates is just an i

The problem here is the PM does not see himself a part of the team, your team, but is on 'other' team that is driven by other gears. The estimates is just an input for his process flow. What's missing is another stream of input that should externalize the constraints and barriers in the flow of both yours and his teams. Even then, as long as PM does not see himself part of your team, all this is in vain, you'd be speaking foreign languages no matter the analogies.