How about 40 insulation pie or polyurethane and then hardboard plywood screwed up. That way you don't have any gaps. It looks better and it's not much more than the cost of tape.
Just a thought.
Or you could make it 1000mm deep using 18mm ply and a 200mm back wall to stop anything falling off the back?
4x2 under the front edge. 4x2 into wall to rest it on.
What about 1x 4 timber glued and screwed to the top and bottom of the 4x2 that way you have a I beam but only loose 1" headroom and 1" height?
Just a thought.
Much better off with 6" joists.
It won't affect your headroom at all as they are on top of your walls.
I hardly think planning are going to worry about 2" tbh.