People pull the move all the time. How difficult depends on how many guns you own. The worst scenario is an accident. No one can safely drive 2000 miles without stopping. If you do it right, and with a second or even third driver, you can go pretty far and have a watchman keep an eye on the vehicle(s). No one wants to move your guns for you. No one will move your ammo. Lets not even discuss reloading supplies.
3 years ago I moved out of our old house into an apartment, 2 storage lockers, and one son's basement. The apartment was maybe a mile away via roads. Only a couple of hundred yards as the buzzard flies. But maybe 500 feet more altitude. And I was living under a 15# lift limit at the time. I didn't move any ammo at all. My son's did yeoman duty on that account. Think a bunch of .50 cal cans.
Guns are kind of a pain. Handguns are fairly easy if you don't mind spending some cash. My approach was to just do what was needed. We went to a gun show and I shelled out a few hundred dollars. But I had a gun rug and a case for every gun I owned after that. Except the boxed guns that moved in other boxes. We moved all the ammo and the guns to my son's house prior to the move out. On moving day I paid the toll to have the movers haul the safes up the stairs. And my wife's piano (cost as much as either safe.) One safe went to the son who was watching the guns, one was left in my garage, and the piano went to the apartment. Confusing to outsiders. The safe in the garage went to the other son's house. His buddy drove up in a pickup, they tilted it into the bed and drove off. Took them seconds!
It all worked well for us.
My buddy and partner at the gun shows had a different problem. His guns were all stored in his funeral home. He had a "false" office. Some were also stored in an old poured concrete building with bars on the windows. His move was more complex. He asked me and I suggested he just go to a thrift store and buy all the old blankets he could (then donate them back afterwards). He had some cases and gun rugs. He even bought more. His trick was to move them via hearse. Wrapped in blankets to keep them warm and unscratched. I think the key is planning the move and being so worried about it that you take extra precautions.
The overnight part kind of scares me. I think you'll need a lot of thought in this part. If you've got the safe or storage room at the other end set up, the driving part is the only scary thing. I know a lot of guys who have crisscrossed the country (military and ex military). All are worried to death about it and they somehow manage.
When your move gets close, ask the question again.