If its an old style Birdy the seatpost slopes back further than in the Monocoque and the seatpost clamp sits on open top of the seatpost. The nature of the clamp is such that there is a limit to how far forward you can tip the seat

When they changed to the monocoque, they made the seatpost more upright and introduced a seatpost that is a bit longer and is closed on top by an offset clamp. With the offset set back, you can achieve a similar position to the original Birdy at maximum height. If you want the seat further forward, you can turn the seatpost so that the offset is forward. In both positions, you have a better range of seat tilt angle.

The seatposts are interchangeable in fact the offset post that came with my monocoque is a better fit in my older Birdies than the original posts are. It also has height markings which is very handy.

I think that if you buy one of the new posts, it may solve all of your problems.

If you look here "Models", they show the new style post facing forwards and back. They also show an old style seatpost on the folded grey monocoque beside the Birdy Orange 9 speed.