After a very long few months - and the passing of my father-n-law, a great friend, and one of the wife's uncles - I am going to be starting to move forward with the rest of the structural parts of the farmhouse remodel. After some playing around with the numbers per the "Design for Bending" site calculator that Don I believe sent my way - basically (2) 2x12 with posts every 10-11ft apart will help in securing the floor joists to be a more solid floor.

To recap: I installed a 2x4 sheathed wall under the main carrier beam the length of the basement. Floor joists are 2x8 SYP spanning basically 13.5ft. I do have a sag of nearly 1 full inch in some of those 2x8s. By using doubled up 2x12s under the basically middle of that span - running the length of the basement and a post every 10-11ft - I believe I can come out with a stronger and more level floor.

My question is - would a 4x4 post or a 6x6 post be better? Or should I go the route of the actual jack posts?

I'm sorry to hear about life's trials.
For something like that I prefer adjustable "BOCA" posts. Not the weak telescoping 2 piece type but the solid type with a screw jack at one end. With those you can adjust small amounts which you may need to do as you slowly remove the deflection "set" of a sagging floor. I know Parker Tie carries them, usually available at Lowes as well.

Thanks Don....that's what I figured