Structural calculations

Hello, I am working on a project where a beam has been specified as a 7x11.875 parallam beam. The issue is that at 11.875, the beam will protrude below the 2x8 floor joists (It's a flush beam). I asked the project engineer to come up with a steel beam design to reduce the beam height. They indicated it would not work. I am by no means an engineer. However, by rough calculation and some industry experience, I believe that a steel beam that is 7x5 with 3/8" wall thickness with a 2x8 Douglas fir attached to either side (to allow for attachment of the joists) would be structurally as strong as the parallam with equal or better deflection. The total span is 14.5 feet. I have uploaded a PDF of the plans. The beam in question is Beam 6 on page S2. See the red arrows. Also, due to file size restrictions, I had to delete a few pages, but they should be irrelevant for these purposes.