Nice clean up of the metal parts.
The space you describe betw the bbl flats and the action flat..
A gap out at the nose of the action betw the 2 surfaces,,but no gap up at the breech face.
You are correct in thinking that shouldn't be that way.
The bolt is pulling the the bbl down hard onto the action flats (water table) at the breech end of the bbl.
The bbl is rotating around the 'pin' in the frame.
There is enough wear to either the hook or the pin (or both) that the bbl s are allowed to sit up higher than they should be. That amt is the gap you can see at the front of the action flats betw the action and the bbls.
Often the wear is from the abuse of 'flipping' the gun open and closed. That bends the bottom of the semicircle lip of the hook on the bbl lug. It opens up the hook opening on the bottom. So when the bbls are closed, the opening is slightly greater in dia. The bbls now are allowed to sit higher,,that's the gap you see at the front.
The locking lug pulls the back end down to the frame if you are lucky to make things feel tight.
Actually things should be the other way around.
No gap at the front and a very slight gap at the back at the breech for future wear. This with a tight lock-up
..and that lever to the right side not way over to the left.
If you carefully move the lower lip of the hook back into position and make the hook a true semi circle again, it will then pull the bbl back into position onto the frame flats.
It will also push the bbls back slightly and tighter against the breech face.
The locking bolt will engage quicker and the lever will lock up tightly with it being farther to the right where it should be.
There should then be a very small gap under the bbls betw them and the action flats at the breech if there is not too much wear in the action. But don't wish for too much!
That rotary bolt,,it's not uncommon to see the small hole in the side where the stem of the yoke comes through a small amt.
Some are just machined that way. The hole is drilled very close to the outside edge.
It doesn't take much fitting/filing to reveal the cavity if you are not careful.
Some people get a little carried away and take too much off too quickly especially with a belt grinder.
The slot in the rotary bolt that catches the hold-open pin gets worn on the tension side from use. That heavy duty V spring puts the bolt under a lot of pressure and when the gun is closed that bolt snaps shut and it & the hold open pin disengage their sharp edges which get worn over.
You can usually peen the locking bolt slot back into good shape with clean sharp edges. The hold open pin also, but sometimes it's just easier to make a new one with sharp edges.
If the pin is undersize as this one sounds and looks like as it is turning side to side, I'd go ahead and make one.
That'll take care of the need to hold the top lever open a little while closing the bbls.
The top '1/2 dia' portion of the pin should be just enough in size to come through the hole in the frame which is blocked off 1/2 dia by the locking bolt. That way the pin cannot wobble or turn & twist side to side.
That keeps the lower locking component lip of the pin in line with the locking slot in the bolt.
The top lever opens, locks and stays exactly where it's supposed to be.
Broken hammers and brazing jobs are very common on SxS hammer shotguns MixMaster hammers are also.
LC Smith hammers are one of the more common types, or at least they were. Sometimes it's just easier to use what you have. Trim up the repair jobs a little if you like and use it like that. The guns saw a lot of use and that's what they were made and bought for.