I wish I could come and help. A 2x6 the length of the wall lagged to each and every stud should do the job. I use the handy man jacks because they have a protruding jaw to lift with. They are dangerous contraptions though, so on another thought, if you could lag a 4x4 vertically on a stud, do this on three places, everyother stud, three hydraulic jacks under the 4x4, you should be able to release the pressure. With the pressure released, using a chisel or drill or chainsaw find good wood on the sill. Cut it off there and remove the bad section. Then cut horizontally the top half of the good sill back a foot or two and take that section out. This way instead of a butt joint, your new sill and old sill overlap giving more connection.
God and family, the rest is icing on the cake.
I'm so far behind, I think I'm in first place.
Premier Bovine Scatologist
Host of the 2015 FAMILY WOODWORKING GATHERING