Nice big room. Sounds like you have it figured out. A raising of the floor to get over the beam, and possibly some additional support with hangers at the beam for the floor joists. Getting the building inspector over is the best way to figure out what you can do, you will need an additional way of getting out in case of emergency. This means an egress, usually a window or a dormer. Maybe A set of stairs to the garage, with a metal door to keep it in fire code.
You could also have a contractor come over with their ideas, work is slow, many guys are lookin for things to do. Maybe hire by the hour if they want. You do some, they do some.
Plenty of options. Good luck.