You're not interested in strength, you're more interested in stiffness/deflection. Properly designed wood and steel beams should limit deflection under a given load. If you're loading them to their strength limit, something is wrong.
I'm not sure a T beam does much for you. Web buckling definitely might be a concern. A standard wide flange I beam might be a whole lot less problematic and easier to source, and give you better clearance.
If you're willing to throw in some intermediate supports to half the spans, you could potentially use a shorter sistered wood beam.
I'd recommend that you speak to a structural engineer about this because this is an optimization problem - finding the shortest beam section that can span the same distance with the same maximum deflection. There are dozens of beams that will be shorter and do the job, you want the shortest. You're not going to get that optimum answer from a chat room. The calculation is not difficult, can be done on a spreadsheet, but if you can't do it then you should get an engineer on it. I'm assuming you'd rather not cause the house to collapse because of a math error.
But no matter what you do, you're only going to be able to shave a few inches of clearance, as beam stiffness is mostly driven by the vertical dimension of the beam. Using steel helps, but it isn't a magic bullet - the beam still needs a certain depth to be stiff enough to do the job, especially with the reduced cross sectional area of an I beam.
I think, for the cost and effort, you'd be better off to cover the beam in yellow protective foam and stencil 'HIT HEAD HERE' on it, or wear a helmet.