I am confronting a similar problem as I prepare to lay about 800 sf of laminate flooring. My floor sagged about 1.5 inches right in the center of the of the main floor living area due to a 4x12 header being supported by a column bearing over the center of single 2x12 20' floor joist.
I removed the load on the floor joist by removing the column and installing a 20' long 4x12 header to support the load of the roof. That reduced my 1.5" deflection to 3/4". I considered floating the floor with a leveling compound to get it level enough to lay laminate, but I will remain too high where the floor meets a 6' sliding exterior door. Also, leveling such a large area will be time consuming, I will have to replace a ½” sub floor layer over the float, and no matter what material I use it will be subject to crushing under a surface load. So, I have decided instead to remove both existing layers of 1/2" sub floor to expose the joist. I will then sister both sides of the floor joists with 5/8" OSB. I don't have a problem with floor deflection now, and ripping 8" wide strips from ply or OSB will ensure a stable plane is established, as the joists are sistered.
Sistering both sides of the existing joist will provide a series of level screeds that can be filed with varying thickness of plywood shims and Fix-All so that when I lay a 7/8" T&G sub floor back down the entire surface is level and well supported. The fix-all accepts screws and nails and has proven to be a durable filler on other sub floor leveling projects I have done.