I'm 6'4", riding on a 60cm Fuji as well.

The hopping is because you are pushing too long on the down stroke. When the pedal comes around the bottom, it can't go any lower, so your down push ends up pushing your hips up. This causes your body to jump a bit, and your much higher mass easily brings the bike along for the ride on the way up.

You can mitigate this somewhat by shifting your weight back a bit, but this will likely have you feeling more scrunched, so I don't do it. I keep my weight forward, and can generate 1700W without a hop.

I would recommend some really high cadence (downhill/small ring) sprints to smooth out your stroke.

Also, work on swinging the bike. At the top of the stroke, the bike should be leaned toward the top foot, and you pull it to the other side as the pedal goes down. This has the effect of lengthening your stroke and allows your arms to generate some of your sprint power (probably good for 200W or more).

Being tall, you want to keep your torso low, and I feel that's a bit easier to do if I'm forward. Another note about being forward: it's much easier to handle lower cadence if you move way forward. It's similar to lifting a heavy box: it's just easier if your hands carrying the weight are closer to your core than if you're holding it out in front of you.