There are "slide pads" that you can get at Home Depot or Lowes that will take heavy weight and which do an amazingly good job at allowing you to slide large, heavy objects.
"I was planning on using drywall to raise it up so it can provide insulation too."
There's an even bigger reason not to use drywall...
If it gets wet, drywall will hold moisture against the bottom of the safe and can, over time, rot it out.
You want something impermeable between the floor and your safe. A thickness or two of vinyl flooring is an excellent option.
Or, you can just leave it on the slider pads and you'll have some air space between the floor and the safe.
"The gift which I am sending you is called a dog, and is in fact the most precious and valuable possession of mankind" -Theodorus Gaza
Baby Jesus cries when the fat redneck doesn't have military-grade firepower.