If this is over a crawl space, adding piers to stiffen the floor system should be fairly easy. Given my shop facilities, I probably would jack to the desired height near where the permanent post is to be, place a precast concrete pad leveled in sand at the post position, measure and make a fixed-length steel post for that location. I think those pads on dry soil will provide completely adequate support.

These floors are 6 1/2' above a post-poured basement. Anything I put under the joists to jack up the sag sacrifices any head room in the basement. I already have a dozen jack posts in the basement under the beams in various locations.

Since these joists are going to have "memories" of this sagging shape, I think it will be hard to jack it up into position. Since you want to maintain headroom in the basement I would put a main beam in the middle of the floor engineered for the span. Maybe two LVL's around a 1/2" steel flitch plate, bolted together. You would cut out a gap down the middle of all the floor joists. Insert the LVL sandwich and jack it into the height you want. Attach the individual joists to the LVL sandwich. This will require temporary support walls, jacking into position both sides of the bisected joists and a few other issues. If there's a second floor involved, it's more complicated due to the extra loads involved. Depending on the depth of sag, expect to patch walls and possible rehang doors.
The size of the beam would need to be spec'ed out by someone who knows what they're doing. This is not a "best guess" project.
Ron

In our last home I had the same problem on a second floor bedroom. Removed the floor and sistered 2x6's to each joist and placed a new subfloor and floor. I could not remove or straighten the existing joists be cause the downstairs ceiling was plastered and looked level. It was very sturdy when I was done. My son had a waterbed in there for many years.

ron and hendricus,
ron-I don't have to worry about doors or walls. The beams that are under each wall have already been jacked level and the walls were reframed, repaired and drywalled. They won't move when I take out the floor. Some of the rooms are near 17' across so, the deflection is pretty exterme in the old joists. I'm pretty much settled on using them for furniture (or firewood) in the next few years. The subfloor is 3/4 tng pine plank, ie garbage. The flitch beam sounds like a good idea but I do want to rid myself of the old joists.
hendricus,
How far of a span did you have for your sistering efforts? I've thought about sistering but the mortised joints move so much I'm worried that the desired result would fall short.
So guys -is my original idea overkill?

12' span of 2x8 and used 10' 2x6. Couldn't go all the way to the ends. If you can remove the old joists and replace with the proper size that is the way to go.
Hank

Inst4ead of bothering to remove the old joist, use a flitch plate and sister a new joist.
You can download Superbeam for 30 days for free if you want to see what various rgades and sizes of joists will do at your span, and it does flitch beams.
The portion missing for flitch beams is the fastener schedule through the wood and steel.
You use enough and correctly sized fasteners to not exceeed about 50% of the cruch resistance of the wood members.
A flitch between I-joists will not be as efeective since the buckling support is reduced, and 1/2 inch plate is probably overkill.

The only hard part about Superbeam is the loading.
Main floors are 40 PSF live, 10 PSF dead for a total of 50 PSF.
Superbeam accounts for live and dead.
If the joist are on 16 inch centers the load per foot of joist (the number superbeam needs) is 40 PSF L * 16/12 = 53.3 pounds per foot L and 10 PSF D * 16/12 = 13.3 pounds per foot D.
Watch out for the wood grades.

The plan you propose would straighten the floor and reduce the bounce. You could also install a series of blocking to further reduce the bounce and sort of unitize the floor. You could further reduce the deflection by putting the joists 12" on center. I did that on a kitchen addition, using 2x10's with a 14 ft span. Solid blocking every 4' or so. No bounce at all. Ends up using 2, maybe 3 more joists.
You could sell the old joists for a pretty profit if you can get them out in decent shape. 100 year old chestnut and oak could pay for the new materials easily. You probably have a few grand in those beams.
Ron