I'm sure you have seen these, but will post them just in case.
videos here on 2 colour brioche in the round.
nothing for flat brioche 2 colour. but perhaps these will give you an idea? or maybe do the hats in the round instead of flat?
Here is a pattern for in the round 2 colour hat ,
video for 1 colour same site.
Sorry I can't give any pointers, I gave up on the one colour brioche even with videos & knitting experience, never mind the 2 colour one. When it stops being enjoyable, i don't see the point in continuing.
My only suggestion, if all else fails, is to change the hats to stripes in the Brioche instead of the combined colours (that way you only work with one colour at a time) and the booties coould be all one colour in a contrasting tone.