You could frame the header into the exterior band,rim or box joist. Whatever you call it in your area.
Since you will be cutting the concrete anyway, you should remove any siding in the way of that area, if you dont' want it cut too. They will have to cut some of the framing also and this is the easiest way to make headroom.
Support the joists in the area.
Remove as much of the band joist you need above the door opening area.
Cut back the joists 1 1/2 inches and install your new header in the floor system.
Basically you are building a flush beam.
Last are the joist hangers.