Wow. I wondered if that is what you were looking into.
Those aren't up to code here. I think that it is just a city code though. They are sticklers about a lot of stuff where i live. Here, the floor joists must have a beam *under* them.
I've heard that pretty much everywhere allows you to do this for ceilings in main living areas where there is just an attic above it. For most homes though, that isn't needed since the roof trusses are also the ceiling "joists" anymore.
A lot of work is involved to do go this route. You would need to support each and every floor joist on both sides of where the current beam is, and then you would need to cut out (as precisely as possible) where you want the beam to go up in to. Then put the beam up, attach the hangers, and remove the temporary supports.
Here is a link with some pictures at the end showing how it can be done. Installing a load bearing beam
If you can somehow live with a beam (or end up having to live with one for code requirements), you could put a metal beam right next to the current beam, get it supported with poles (obviously a lot further apart than your current ones and would need new footings), and then remove the current poles and beam. Would solve the pole issue probably, be less work, and probably less cost that all of the materials and labor to do it the other way.
I moved a 12 foot beam in my current house to accomplish what you are thinking with the joist hangers. I didn't want it right above where my wet bar was supposed to go. I ended up turning my home theater wall into a load bearing wall that was about 3 feet to one side of the beam. I made another temp wall (with studs right under the each floor joist), and then moved my wall beam over 3 feet away from the theater. There is duct work right in that area, so now it just became a part of that framing. Obviously I built up supports for each end, but they ended up inside what were to become walls and thus never be seen.
For the other beam in the basement that ran about 20-25 feet, I just lined up a wall with it to be a part of our office and bathroom.
I love the look you are going for without a visible beam, but unfortunately for you your beam is right in the middle of the basement.