Q: How do you figure out which engine mounts actually need replacing?

With all most 200k miles you most likely have all four mounts needing replacement. The first thing to do is to physically look at each one and look for rips or tears in rubber, sagging or oil soaked. Once all are checked by looking at them then have someone look at engine while putting engine in drive or reverse and give it a little gas with brake held. Look for excessive engine movement indication broken mounts on side that lifts up.