It used to be a note or something in the IRC that said something to the effect that if the joist butted you needed to place a strap across the top. I'll see if I can find it.
I have placed steel plates on top of concrete columns after the concrete was poured in the tube and vibrated. Fill to capacity and place plate, rattle the place to be sure the concrete is filled in around the studs. Just because I have done this does not mean it is right but it seemed to work.
I would add a couple inches to the top also. Have done this in the past without a problem that I know of. The top layer of the existing is definitely going come apart. Also will be a dust problem unless sealed with a thick sealer.
I would not call and open that can of worms. Most all of my experience has been in equipment maintenance and modification. I have not ever needed a permit. Most of the work by us was in MD PA and SC.
You cut blocking the out of the floor joist material and place along the joist header building it out past the depth required for the column or post. The blocking rest on top of the post from below and the next post above rest on top of the floor material, I think you said 2 x 6's laid flat.
A photo would be nice but I think I understand what you are after. How are you going the handle the hole where the wire is? Are you going to have to pull the wire and redrill the hole? I have fixed situations like this before with 1/4 inch steel plate along the bottom vertically, 4 inches tall...
What is the area of the plate? How much load? Are you going to grout in place or is lt going to be able to be lifted and set in grout bed? Can shims be used instead? What is the plates sitting on?
I find these worth their weight in gold. Pulled me out of many a problems on power presses.
http://www.ringfeder.com/en/international/products/ringfeder/?g=382
I've seen water freeze in pipes of all sizes, unconfined and confined, break open. I've seen scaffold legs get water in them that were plugged with dirt freeze and break with the top sides open. Don't know how this relates to what you are doing.
I've never a slope that long but we always went from top to bottom. I'm not sure why. Even when we were doing steps or stair runs we went top to bottom.