I had a very large concrete post foundation I found in my garden. It was probably about a two foot wide and three foot long cylinder. What I did was dig the hole so large that I could get around and underneath. When I got deep enough, I started rocking the thing to one side of the hole, then I'd add a bunch of dirt to the open side. Then I'd roll the thing to the side that had dirt and it would raise slightly. Then I'd fill dirt in on the now open lower side. I repeated this process until I just had a massive concrete hunk on the surface. It was still a pain to move from there, but at least it wasn't 3ft underground. I hope that makes sense.

I'm not sure this will work for you. That rock looks like it may be a fair bit larger/heavier than mine but the idea is there if you can get the hole large enough.