I think you are correct Neal, exactly what I would do.
Don’t worry about the old rivet  holes, they won’t line up, I would put in new rivets between the original ones and then put rivets through the old holes if possible mainly just to plug them. That is what I did with my Rocket.




 

From what I can see from the pics, looks like the angle of the vertical edge,of the brace dididnt match the angle of the transom, heavy at the bottom, they put it in and someone stepped on it to push it down to rivet the horizontal and to the front end, Ray's suggestion of removing the brace then straighten the transom an refitting the brace would cure it, might have to take some meat off the the rear horizontal edge that rivets to the bottom of the "T" stringer or the bottom edge of the vertical, allow it to lay natural with no stress against the transom, just my thought, what do you think Ray 

You may have to completely remove the brace.

I think I see what needs to be done. 
1. Drill out the rivets in blue.
2. Remove the front bracket in red.
3. Massage the transom back to flat which will move the brace forward
4. flatten the front bracket. 
5. Reassemble.

I just can't figure out why they built it that way.

Here is the front of the transom brace.



 

I’m sure they built my 56 Rocket with a big hook in the bottom, I drilled all the rivets out of the transom braces and moved it all where it should have been and then doubled up on the rivets when I riveted it back together.The bottom being flat is more important than the transom being flat,, but getting the wood to fit is going to take some work.

The bottom is pretty flat. There is a section about midship that has a dent in it. 
 

And yes, it does look like it was built that way. It looks like they installed the transom brace first then forced the transom to fit. The brace is too far back.
 

Is the bottom flat?
Does it look to you like the factory put it together that way?

Here's what I'm working with... Looking straight down, here is the transom from the inside. You may be able to see where the brace is bulging the transom outwards near the bottom of the transom.
 

Here's the bulge from the outside:
 

And here's the bulge from side to side. 



I'm thinking I'm going to install the inside board to keep the top of the transom in shape. Then fit the outer boards individually and not put them together first. 

Hey Trey, i find it best to fit and mount everything first, make any modifications necessary then go ahead with the finish. It helps too to get some sealer inside the bolt holes as well sealing up the raw grain in the holes, cheers bud have fun