Installing roof joist into header plate?

[GardenofficeDIY]

Hi looking for advice on dealing with the 2.5m height restriction on a outbuilding. I am building a garden office 4x2 stick frame.

I am looking at installing french doors (2400mm wide) and I underestimated the Size of the vertical header plate required.

If I go for a 8x2 vertical header doubled up, it throws my already tight height calculations off.

I was planning on birdsmouthing the roof joists so they sit on the top plates at either side of the garden office.

However to save some height could I use joist hangers that are attached to the vertical header plates, to hold the roof joists (6x2 over a 3000mm span @ 16” OC)?

thanks in advance!