Do I keep it? Or trash it?

Because the 340 has a larger bore than the 360, I'd be inclined to keep it. Don't know if you plan to bore the engine out further than stock specs. Don't know what your end use is for the engine (daily driver, race, show car), nor do I know what heads and crank you plan to install. I'd avoid boring out this block if it's going in a race car.

Most LA stroker cranks I've seen can be had with either 340 or 360 journals. For the same stroke, the 340 will be larger.