I think to expect to create 400 square feet of new space for $50 per square foot is a pipe dream, especially when doing major stuructural work within a garage. Adding new beams is a fine idea provided that there are footings that can carry the concentrated loads created at the ends of the beams.
Depending on the lumber species and grade that was used for the existing ceiling joists, 2x8's can usually carry up to 12 feet or so of floor load, so only one beam will be necessary, but the loads at the ends of the beam will be high.
I don't know what your garage or attic ceiling heights are, and I don't think 14-inch composite joists will span 20 feet and perform acceptably. These joists can be very bouncy even when structurally adequate, so deeper joists with wider flanges may be called for.
I think that clear-spanning the garage is the way to go for economy, but the height problem has to be solved, and the method of bearing the new joists on existing walls has to be dealt with. A 16 or 18 inch joist will not go where a 2x8 is or was.
What you really need is a competent architect or structural engineer to investigate the alternatives and advise you, and work out the details before any demolition or construction is done.
Architect (NY) and Home Designer (PA)