So throwing 1800kg 3m is not easy. It takes an extraordinary amount of force to do this. The first question I would have is why your creature evolved to have this capacity, but that's outside of the scope of the question so we'll ignore it for now.
I look to shot put, rowing, and other similar sports for some inspiration. In all cases, the motion starts with using strong muscles (like the core and the legs) to start the motion and impart as much force as possible, followed by using the weaker muscles (arms) to get what they can out of the motion. I would expect similar. I would expect to use as much of the core and legs as possible.
So can it be done? Well, I think it's going to look more like a jump than anything. When you jump, you impart kinetic energy into your body. If you do the math, distance jumped scales linearly with the energy imparted into the jump. If you have to impart 8x as much energy because of mass (7x bodyweight in lifted weight plus 1x yours), that's equivalent to jumping 8x as far with just your normal bodyweight. Thus, your creature needs to have legs capable of jumping 24m. The human record for a standing long jump is 3.73m, so you're looking for a creature whose legs are 8x more powerful than ours. And I mean power in the dynamic sense here, not just strength. You're going to need 8x the fibers, so these are going to be beefy legs.
After doing this "jump," we need to arrest our movement. Why? Because you asked for a non-jumping solution, so we better end up where we started. To do this, we will push off the rock. This will impart some more energy, but it'll be pretty minimal. If you really wanted, you could do the math. You just have to push off with enough force to arrest your motion. This happens to be roughly enough force to jump 3m. So your creature's arms need to be about as strong as our human legs in order to do the job.
So now we have our creature's biology. If I do the math and put it in terms of my own body, the creature needs to have 2 legs, each the size of my torso. It then needs 2 arms, each the size of my legs. For a creature that's only 600kg, that's going to be tight. You're going to have to trim some mass elsewhere. It probably has a very short torso (which also helps for the lifting).
Your creature is basically a genetically engineered rock tosser whose sole purpose is to throw these 2 ton rocks around.