I have a similar set up with beam and joists, I just added supports
and thick plate steel under the beam the leveled it slowly. Why do you
need a new beam, why cant you just add supports to what you have. When
you start jacking to make it level things may break, I had a few
joists I had to sister on new joists but your idea of removing what is
there is full of risks you cant imagine, like everything failing
completely, the money and time you will waste in proper jacks to
support everything while removing the old beam is taking a little job
and making it major.

Yeah, that's what I started to realize. I figured it would be simple
to replace the existing beam, but I think now that this is full of
traps and a much bigger job than I expected.

I don't need to replace anything, I'm trying to get rid of a column in
the basement. If it's too complex/expensive, I can live with the
column there. Currently, I'm still looking at the different
possibilities to assess their complexity and cost. I'll take a
decision once I have all the info I think I need.

Getting some external insight is very helpful for taking this
decision.

Thanks for your comment.
Phil