@0die - Yes!! This is basically what I had pictured for mine, the "house" and "coop" with free movement of each other. Except mine would open into yet another bigger, fully-but-less-securely enclosed big day run. Can you clarify how big the "house" aspect of yours is? If I'm looking at the pic correctly, seems 4' x 6'? The one I mocked up in my picture was only 4' x 3', but that was just a guesstimate that now seems too small.
the "house" is 3x6 floor and 4 ft tall outside dimensions. But that includes 3 separate areas.
roosting area is 3x4 floor and 4 ft tall with 2 rows of 4ft bars.
3 nesting boxes, each 1x2 and 1 ft tall
storage area 3x2 and 3 ft tall accessible from the outside.
each of those areas is actually slightly less in interior space since you have to account for thickness of walls, floors, beams, etc. remember, when everyone gives you dimensions they are probably measuring the actual size of the structure and the lengths of lumber that were used. Actual interior volume is reduced buy the thickness of each board used.
technically, I guess my "house" is really the same as your 4x3 house since your egg boxes are hanging on the outside and you probably don't have a storage compartment.
4x3 might seem small for the house but in my climate the chickens will not roost inside in anything less than gale force winds a hard cold or freeze. They roost out in the open air coop. And the house has excellent screened ventilation windows on 3 sides and is usually wide open to the coop so it's more of a carport.
I have 10 birds right now and there is no lack of space at night since the coop is 6x12. I could probably add a few more birds without issues. The day run is quite large plus I let them out in the front yard if I'm outside.