Replacing Old Ceiling Joists
 

My house was built in the 1950's with a flat roof. In my garage there is a set of exposed ceiling joists that make a cross. Attached is a quick drawing of what it looks like. The problem is that the space perpendicular beams that sit on top of the header and the joists is a bunch of unused space. What makes it worse is that the joists are at an angle so it goes from a small amount of wasted space (about 6 inches) to 2 feet to rest above a door header and another supporting header. I know these were added as a part of the structure. I was hoping to replace these with something that would return that space to me so I can mount a ceiling bike rack.

Any Suggestions. I can get some pictures if further detail is need.

These angle braces were put in to keep the building square or to make it wind resistant, we should be able to figure it out let's get some photos.