What are the options to increase doorway height in load-bearing portion of foundation wall?
There are two very important dimensions left out of the "Obstruction Details". See picture below.


Overall height of overhead clearance. (Directly related to number of courses of cinder blocks in the wall). 
Width of the opening. (This is of lesser importance than the overall height).




The dimensions I show are just pure guesses based on what one may expect in a fairly standard basement.

If your basement was built with 10 courses of cinder blocks such that the joist plate is directly over the bricks then there are going to be many fewer options. Already with severely compromised ceiling height the engineer may suggest a cross support beam inline with the wall fitted up between the ends of the joists that are cut off flush to the surface of the cross beam and then supported via metal joist hangers into the sides of the cross beam. Such cross beam would span over the opening and extend to an even multiple of the joists spacing.

If your basement was built with 11 or 12 courses of cinder blocks then you have more options. The engineer may suggest cutting out the bricks and overhead cinder blocks and laying in a cross beam header. This header would be longer than the opening width and may be specified as a steel or wood beam. The ends of this cross beam header would be supported by the first solid cinder block course on either side of the opening. It may have to be shimmed up from the cinder block course with wood or bricking.

With either of these approaches it would be necessary to prop up the overhead joists back away from the opening whilst the engineer approved re-work was being performed.