That is a 360 external balance damper.

If all you want to do is start it to see how it sounds you can use the 318 flywheel. It will have a vibration however just to run it to see what it sounds like it will not hurt anything.

Found One on Facebook
Cant believe it popped up out of thin Air

By looking at the guys profile he goes fast so it probably is in balance.

The magnum balancer is about 1/4" or so thinner than the LA. The hub itself is still in the same plane as the LA however so the pulleys would all line up if you swapped the timing cover/ water pump/serpentine drive and all. Magnum heads have 10 bolt valve covers but the LA covers will bolt on them. I have LA covers on my magnum heads as well as all the front drive system on my LA block. The magnum flywheel would have 8 notches on the back side for the crank sensor to read, the LA flywheel does not. Magnum heads also use the 5/8 hex spark plugs where the LA uses 13/16 hex. Also the bolt bosses at the ends of the heads are not the same so you may need to fabricate a little if you want to run all the LA accessories with the magnum heads. Putting the magnum accessory drive system on an LA headed engine is not feasable.

The down and dirty way to make a 318 crank work on a 360, is to tack weld the balance weight off of a 360 torque converter onto the flywheel. Run it and see if your vibration is gone, then weld it on better. Did it dozens of time with cast cranks when we were circle tracking. never had one fly off. Jim