A speed related vibration is almost always wheel or unjoint related. A bad alignment will not cause a vibration directly but it can cause irregular wear in tires or cupping etc.Regardless. It always happens. Doesn’t matter if it’s in gear or neutral, engine on or engine off, touching the brakes or not touching them. It’s strong enough to shake the whole car.
I honestly would pull all your wheels and dismount the tires. Spin each wheel on the balanced and make sure the plain wheels are not out of balanced. When I bought my cruiser it had some stock sized tires on it. I drove the truck 2000 miles home and had a very cyclical vibration. Finally stopped and had the wheels and tires rebalanced and thought it was better it wasn’t gone. When i got home I put all new tires on and the problem went away.
The only other common issue would be an out of phase u joint or some odd driveshaft angle problem or lack of grease perhaps