Is a sandwiched beam made out of 2x4s laid flat a suitable for a 15' span that doesn't carry a load?
If you put a beam across the room you'll feel bad every time you look at it.  if you have a flat ceiling, you'll feel proud.

Use joist hangers to put some 2x4s between the ceiling joists so that they pass just above the 2x6 (stuff's going to sag), drill through the top plate from below with a spade bit and screw the 2x6 to the 2x4s remove the wall and top plates patch and plaster the ceiling.

If you can't get into the ceiling to get enough access to fit the hangers you could just lay 2x4s across the top of the ceiling joists and use really long screws, or maybe even come through the roof with threaded rod.