Special Tool For Lifting Needed

pwrbildr

While this is not exactly a tool designed for lifting, if it will pass an osha fall protection inspection, I would trust it to hold up a 6,000 lb. rock.

Concrete Anchorage Point

A little over your price range but it does allow you to do everything from the top side of the boulder which to me would be worth it.

TempestV

with 10,000 lbs capacity, a safe working load is going to be a touch over 3000 lbs. Depending on how it grabs the slightly different surface of the rock (it is designed to grab concrete), it would probably lift a rock that size fine, but over time, I wouldn't be surprised to see it fail one day.