343 bore

Just for giggles, lets say your 343 makes 280 hp.
Better heads and bigger should be a linear change
to about 294 hp if all things are equal. Peak torque
should rise a bit due to the longer stroke.

if you are talking about a set of Edelbrocks probibly notmore than a set of stock 1970+ dog leg heads.

 This 343  is a whole new ball game, ain't it? I have been going through the same thought process over here with mine. After talking with a few folks about it I have decided to just make the 343 breath easier and replace what needs to be replaced. Like everyone is saying.... to modify it, it's going to take some time and money with more than bolt-ons. The options made my head spin.
  After getting right down to it, deciding I'm not gonna be drag racing this car,  I can add just a few HP to it to help it get some better mpg. It is all that can be done to make it dependable. This is where I have decided to concentrate my efforts.
 I'll take dependable over an extra 50 HP all day long. I'd rather drive it than keep tinkering with the modifications all the time. AMC built dependable cars from the factory. I'm not good enough to mess with perfection.
 Wish I was closer.  Sounds like we are almost right at the same stage with the same engines. I haven't measured my bore yet but I got the car with 80K on it. I am hoping a clean hone will do it justice. Keep us updated on the direction your going in. I'd like to know how it goes.

If you can find a 390 crank, pistons and rods, you can usually bore a 343 out to that size and turn it into a 390, always a good idea to sonic check first though.

360 crank is a good option, just be a little careful to check deck clearance though as the 360 block did have a slightly taller deck height for a reason.

Biggest downside to maintaining stock stroke is the pistons are a long way down the bore, which doesn't make for an ideal combustion process, i.e. no quench.

Dogleg heads will help, most of the gain comes from better exhaust flow, probably not a massive gain there.

Edelbrock heads will give similar gains to mildly ported dogleg heads.

How much cam you want to run is largely going to determine the output and how you tackle the rest of the build.

My 343 with 360 crank and Edelbrock heads is making around 260HP at the tyres and runs very close to flat 13's in the 1/4 mile with the BW auto and 3.54 rear.