I apologize for the delay. I was traveling and just returned home.
The bridge idea is reasonable, but the beams would need to be extremely large to make that work.
I would do beams on the floor, similar to the bridge you're talking about, but lay them directly on the 4x12 joists. Then, in the basement, shore the joists directly below these rail beams.
Hello. Do you have any other questions for me on this topic? If you could rate my answer, I would appreciate it.