Ive got some experiences moving boxes so I will chime in. First of all this shouldn’t be your financial obligation, Any shop worth its salt will pay to have your boxes moved for the opportunity to have you work for them. (That’s what we do) Just ask them. Guarantee they will say yes. As a business owner I have always offered to take care of that. If you are willing to invest in tooling then I am willing to invest to get that tooling into my store!
Second cribbing is your best friend here. A lot of these old wood or thin aluminum beds can handle the weight, but not as the load of a snap on box is distributed. (Through those thin 4” wheels). Once it is loaded just crib it for the ride and your ok. Keeps everything stable.
Third empty out your socket drawer as it is the heaviest, puller drawer if you have one too. Pelican cases work really nice for this.
When I closed my Naples store I sent everything back to my expanded Chicago store, part of that equipment haul was a 12’ long Mr Big and a couple of my roll around carts. Made the trip flawless.

Pelican case has all the sockets and puller’s in it.

Wheels removed from Epiq cart and paletized.

Yes a MR Big can be carried with a forklift!

All my tools loaded up and on the way
Now yes I am aware that everyone has different budgets, timeframes, etc. But I am the most **** person that ever walked the face of the earth! If I can get all this stuff scratch free accross country anyone can. Don’t bet nervous and don’t overthink it.