Sorry, just saw the post. It's been busy in the shop.
All of the production Magnum heads are the same. All Magnum heads are a closed chamber design. The 318 Maggie started in '92, the 360 in '93. They ran through 2003.
The '73 340 is a low compression 340. Those should be flat top pistons in there, but over 40 years other parts could have found their way in. Confirm they are flat top, not the earlier domed pistons that gave the '68-71 340 higher compression. The domed pistons will not work with closed chambered heads.
The Magnum heads use pedestal mount rockers that oil through the pushrods, not shaft mounted rockers the LA motors had. To run the Maggie heads the lifters need to be replaced with ones that will oil through the pushrods. Most aftermarket Mopar lifters are setup to do this. They are shared with AMC.
The head conversion requires different pushrods. Mopar Performance sells a kit for the conversion, but they are a little on the short side. You are better off mocking it up, measuring the correct length, and ordering a custom set from somebody like Smith Brothers.
The Magnum intake bolt pattern is different from the LA heads. You can either redrill the Maggies (make a jig off your old J heads) or go to something like a Mopar M1 or Edelbrock RPM Air Gap intake for the Magnum heads.
The Magnum heads have a tendency to crack between the valves. They don't tend to go through to water, but some do. When 'yarding, grab the lowest mileage one you can find.
As several other people have posted, if you are grabbing a complete Maggie out of the yard, I would strongly consider using it instead of the 340. Some restorers will pay top dollar for a 340 block (usually the '68-71's though). If your 340 needs any other machine work, I'd be building up a Maggie 360 to go in there.
We've built a few for friends and customers. With a mild cam (268 adv duration) and street gears they run 13's in the quarter all day without breaking a sweat.
Most of the Magnums I've opened up are very clean inside. Only the neglected ones were ugly. Even on some of the ugly ones the cross hatching was still visible in the bores.