I've moved and set all the machinery in my shop including CNC mills, surface grinders and hydraulic broaches as well as floor lathes using the pipe/rod method of moving.
I would suggest instead of iron pipe (which might impart a texture from the pipe's surface in to your floor), to use drill rod or semi finished hot rolled rounds, 1.5" in diameter to 1.00" in diameter. The larger diameter, the easier it rolls and the surface finish on the rounds won't leave an impression on your floor.
Using the pipe/rod method and 2 men, we've moved machines weighing upwards of 9,000 pounds, way more than your safe and I agree, I'd move it with the door attached and latched.
We put a friend's huge Cannon safe down his basement stairs by laying down carpet, removing the basement door, cinching a stourt rope around the safe and with 4 guys on the rope, we lowered it down the stairs, sliding on the carpet. Not at all bad.
A few more beers and we would have 'let her rip' and that would have been ugly......
Newton's Law (a body in motion, tends to stay in motion until impeded by an immovable object) would have applied as it hit the basement wall. Luckily, we restrained ourselves............