Congratulations on the new house!
If you're transporting your collection yourself and you're driving, you don't even need to tape down the potting mix as long as the vehicle, or trailer that they are riding in has good suspension and you drive carefully enough to avoid hitting potholes and giving them a very bumpy ride. Although, very newly potted plants might benefit from a bit of tape to hold their roots and the new mix in place for the trip.
Simply get yourself some big boxes (about the size that would hold a large microwave oven...anything bigger becomes too heavy), line the bottom with a couple layers of plastic (such as a couple unopened garbage bags), to protect the cardboard from moisture coming out of the bottoms of the pots. Moisture will weaken the bottom of the boxes; so, they must be kept dry to retain their strength integrity. Also, add a few extra strips of tape across the bottom to give it a bit of insurance. A box with one strip of tape along the seam on the underside of the box might give way when it's full of heavy plants. Pack the plants inside the box tightly...each pot pressing against neighbouring pots. I say "tightly" because if you put them in loosely, they'll wobble and shift around......and there will be a LOT of damage to the foliage from the friction. Take your time to pack and put them in like sardines. If you're short of room, you can even pack larger pots in the bottom and then put in bits of cotton batting (purchased at a sewing supply and fabric store), inbetween the foliage of those larger plants and then put smaller pots on top of the cotton batting. Anyplace there is a leaf or stem that you are concerned about, pack a bit of cotton batting around it or inbetween it and it's neighbour. Then, you can layer more cotton batting on top of the smaller pots and put a layer of small plants on mounts, or small pots, into the nooks and crannies, all the while, adding more lumps of cotton batting as you go. You'll literally be layering the plants, like sardines in a can, on top of the plants below. But, if you pack tight enough and use plenty of cushioning, they'll all make the trip in great shape and show no damage at all. They will arrive in perfect shape, assuming you do not drive at 100 miles per hour over seriously uneven road surfaces at a construction site, etc.
Your trip is a similar distance for someone here.....say.....in Windsor, Ontario who is driving to the Montreal show to put in a display. That's about a 10 hour drive, not counting stops. Other than packing plants tightly so that they do not move, or wave around and rub on other plants/surfaces, the distance is really not a concern. You can stabilize tall stems by packing the plants tightly and then crossing the stems and tying them together with some electrical tape, or scotch tape, or even pipe cleaners. It's best if you connect 3 or more stems because a triangle is the most stable shape to prevent movement. Of course, at the unpacking end, all the stems need to be carefully untied and freed before you begin to remove plants from the boxes.
You can also go to the seafood department of your local grocery store and ask them for the styrofoam boxes that the seafood comes in. They usually just throw these out. A quick rinse and the smell is gone....especially if you use hot water, or you can let them sit in the sunshine for a few hours. But, usually, even just rinsing with cool water and letting them dry will remove any odours. Then, you can use these boxes to pack your plants. The small pots are packed tighly, using cotton batting where it seems like a good idea and cover them with the lid, which will snug down tightly; but, you can tape it shut if you feel the need. You can stack these boxes in your moving van/truck. The larger plants can be packed tightly into the boxes; but, they'll be too tall to put the lid on. But, if you choose the height of the plants carefully, you can put another box on top, upside down, to create a double-tall box. Use Tuck Tape (red tape found in hardware stores and sold for taping vapour barier when building homes), to connect the two boxes together. That tape is the MOST sticky and strong of any tape! It puts duct tape to shame. Once you've taped two boxes of an identical size/shape together with the Tuck Tape, you can also stack these. If you need a box 3 times as high, put two boxes together as described above and then cut out the bottom of the top box. Of course, now that it's upside down and taped to the box below, it's bottom is the top of this new double-height box. Anyway, cut out it's bottom and once you're done packing the really tall plants, put a third box, upside down, over the top and tape it in place. Now you have a triple height box full of plants and you can also stack this, too. For the boxes to be strong for stacking, don't be cheap with the tape. Use enough tape to make sure that the boxes that you are connecting are very well attached and not going to come apart. Of course, when stacking boxes, be sensible. Don't put your bowling ball collection on top of the styrofoam fish boxes that are packed full of your plants. Stack styrofoam boxes on top of other styrofoam boxes and put the heaviest ones on the bottom; or, pack other lightweight things on top of the styrofoam boxes. I use these boxes to ship plants across the country. They arrive in fine shape; so, they can handle normal wear and tear/abuse. Like I said, just be sensible and if someone else is packing the vehicle, make sure that they have some common sense and they understand what's at stake.
Or, if you leave the tallest plants just open to the air, you can jab thin bamboo sticks into the sides of the styrofoam boxes to provide supports that you can tie your tall plants and tall stems to. Of course, using styrofoam boxes means that you don't need to worry about water weakening the box bottoms. If you start asking at the grocery store now......and check with them each week, you can collect a nice selection of great styrofoam boxes to use in October. Whatever you don't use up can simply be thrown out, recycled or given away before you leave your old home.
Good luck.
