I believe you can use the 340 engine mounts on the 360, but not the other way around. My challenger had a 318 which I swapped with a 360 and I want to say that I spun up a small aluminum spacer to make up the width difference. I'll try to check tonight when I get home, if I can find the mount. Car's in pieces right now, but I think I know where the mount is.
I concur with everyone else on the B&M flexplate. I internally balanced the backside of my 360 so I wouldn't have to worry about special flywheel/flexplate/torque converter balance, but the aftermarket flexplate is a decent piece. Converter bolt holes may be a different size than stock, but I don't know this for sure.