Moving Orchids 100's of miles

There are two aspects of your question: actually packing and moving them, and making sure they get the right conditions upon arrival. The latter is on you, but having moved orchids from GA to KY to SC to NJ to PA, and upcoming move to NC, I'll offer a few tips.

Considering the heat, I suggest the plants be watered thoroughly a day or two in advance of packing them up. (If it will be cold, don't.)

Anchor the plants well in their pots. Wobbling about in the pot is a perfect way to break roots or do worse damage. I use newspaper or paper towels to fill the void space in the top of the pot, or at least to cover the potting medium thoroughly. Use masking tape liberally to hold it tightly in place.

This time of year, keeping the plants from cooking en route is a big concern, so several layers of insulation is key. After anchoring the plant in the pot, if you can, surround it with shredded paper as padding and insulation. "Easter grass" works if you don't have access to other sources.

Whether you pad it with shredded paper or not (doing so provides another layer of insulation, so is better) wrap each plant with multiple layers of newspaper, forming something of a cylinder, closing the ends and taping them.

Place several plants in a box, close and tape it.

In that process you have several layers of insulation - the box around the wrapped plants, the multiple layers of newspaper, and the shredded paper are all barriers to prevent heat from getting to the plants.

If you ship the plants, I suggest a quick delivery service to minimize potential exposure. Personally, I'd use either FedEx or UPS and have them shipped to one of their stores, so they'll be kept indoors upon arrival.

If you do as I did, and rent a truck to move some of your other stuff, put the boxes on the floor of the truck, which will be the coolest. A rented trailer will not be as friendly, as there want be enough volume for temperature stratification. No matter what, do not allow direct sunlight to ever hit the boxes, as that can cook the plants in no time. That is a particular concern if your collection is small enough to transport by car, as even in air conditioning, sunlight can heat boxes.