RE: 340 or 360?
Your 340 sounds similar to the one I built for my Duster: .040 over & decked block (11.3:1), ported & polished "J" heads (2.02/1.60 valves), .510 cam, roller rockers, Mopar M1 intake, Holley 650 double pumper. This motor pulls real strong, especially on the top end, but it's a bear to drive on the street. I'm thinking of detuning it slightly with a vac-secondary carb and a a tighter converter (I'm running a 10"/3500RPM one now), and losing the underdrive pulleys which are causing grief with the charging system.
I guess it all comes down to what you want out of it and what kinds of compromises you're willing to live with. Mine is a toy that I drive infrequently, and only on the street, but I'd drive it more often if it were a little easier to live with.
As for deciding between a 340 or 360: I'd go with the 360 (or a stroked 340) in a heavier car that needs more torque, but in a lighter car, I think the 340 would work better since the big bore/short stroke lets it rev easier, and it has a better rod/stroke ratio. 360's are cheaper and easier to find, but 340's have more "status" as they were only sold by the factory as performance engines. Again, decide what's more important to you.
Brad