My wife bought a 1930's 2-story A frame farm house. The framing is all oak. We had to gut the drywall (PO replaced paster & lath) due to old mold and mildew. The wall studs are 2x4 (2 x 3-1/2 actual), 18" on center and the second story joists are 2x6, 18" on center. The floor joists are supported by 4x4 blocking between the studs.

I have a supporting wall opened up. This wall is between two rooms and supports second story joists for a room that runs the length of both rooms (approx 38'). My question is, while I have this open, would there be any benefit to adding a 12" 2x4 ledger under each edge of 4x4 support? I don't have any sagging at the 2nd floor supports. I do have to jack this wall about 1-2" back into place at the sill plate below the first floor due to a failing and poorly repaired foundation.