Good start!  Strap it on well. 

A heavy machine tool can be rolled across a floor on short lengths of pipe (I've moved a large milling machine that way).

Having padding and a few appropriate long levers helps.   

Sliding across a hardwood floor can be done too - using a rug.

Just think it through step-by-step.

Open pickup?   Four real husky guys can manhandle it into the bed, lying on its' back.  Look up the "forearm forklift" that movers use.    

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I've moved a Brunco wood furnace that weighed about the same, and about the same size and shape, using rollers cut from iron pipe, and crowbars, all by myself.  Getting it home I used a low-deck trailer.  I did have help getting it on, but got it off alone. 

Have a few 2x4's ready also.   In fact, making a 2x4 skid will be a good idea.  Rollers can also be made of 3/4" heavy wall PVC pipe, or broom handles.   
 
600 lbs. is a mighty heavy load for a refrigerator dolly. IMHO.
Let that much weight rock over-center and you may find yourself overmatched.   

In my career I moved many, many machine tools, some weighing upwards of 40,000 lbs.   Go slow, think, and plan.  Don't use brute strength instead of proper planning.

Many decades past I was party to moving several large mass spectrometers and similar large analytical instruments. Happily we had access to small teams of "little guys" known as riggers. Their motto was basically "brains and things -- NO strain". They came with a bunch of "sticks", ropes, chains, hydrolic gadjets, etc., etc. They made it look easy, and it was, for them. They never broke a sweat.

Grisen

I am thinking moving it around wouldn't be too tough. Getting it on the truck, tilting it back and sliding it in would be the problem. I am thinking the small tilt bed trailer I haul my XMark Zero turn on would be my best bet. It is pretty low to the ground and I could slide it on and off much easier. Would feel better if I could lay it down on the trailer but not sure how hard it would be to do that. If the door comes off it would help. My XMark weighs 800 pounds and I have drug the back end where the motor is around in my yard enough to get it unstuck on more than one occasion so two guys should be able to slide it on a concrete floor. Pipe rollers are an easy option.

The best advice I have ever seen suggested on moving a safe was this: go out and buy a case or 2 of beer, invite a couple of friends and then hire a reputable moving company and you and your buddys set and drink the beer as you watch the professionals move the safe. 
Yes its a bit on the expenisve side but in the long run your well ahead of the game. I had to have my safe moved from my garage into the house, that involved just one step and trust me, it was well worth the money spent to hire professionals to do the job. 
If you have any doubts, just think of the damage the safe will do if it falls over and hits someone. 
Sam

Don't forget short pieces (3) of PVC pipe for final placement.  Better than having golf balls rolling around.  By the way, it cost me $360 for pickup/delivery (15 miles) and getting it up incline driveway into garage.  It wasn't cheap but had no choice.  Friends are more banged up than me (they're only good for alibis, not moving bodies).

Also, my mix of 15 ARs, SS, bolts actions, shotguns, etc., would not fit properly on one side (24) without "rifle rods."

Why not use the other side?  Wife claimed most of  it.

I moved one down into my basement, after getting it off a local ad. Went with my truck and backed up to the guy's garage. Lowered the tailgate and used a winch to pull it out of the garage on four 3/4" schedule 40 pipe rollers. Just kept moving them to the front as they came out the back. Once to the tailgate, I moved the strap from down low, to up high, and took the rollers out. Then gradually pulled it over on the tailgate, and then up into the bed, laying down.
When I got home, I put a block in my garage, and used a pulley to pull it out of the truck, and then pull with the strap to stand it up again. Picked it with my engine puller from the middle, so it hung horizontal. Then pushed it over to the basement door from the garage, and lowered it down on the landing. Using the strap again, I hooked the winch on again, and used a snatch block to go from outside the garage, and lower it down the stairs. As it was on the landing, I put one roller under it to allow it to roll a bit, and tilt to slide down the steps. I gradually allowed it to move down off the landing until it was headed downstairs, and then slowly lowered it down to the basement. 
Once it was in the basement, I gave the bottom of the safe a good coat of automotive wax, to make it easier to slide. Had a friend come over, and we pushed it around a corner, and 15' into my gun room. It actually wasn't hard to push with the waxed/painted bottom. Never anchored it, as I figured nobody can ever get it out of my basement easily!