here's some homework then.

take the 'birdbox'.
remove the end where the lid slides in.
Then create a seperate piece that glues there (two cubes one on top of the other would do it).

That way you can orient the box on the bed with the grooves vertical for easy printing and print the lid and side flat and seperately.

That's what I was going to do - but I got sidetracked, I frequently get sidetracked for days, sometimes years...