How can I effectively transplant a saguaro cactus?

One component of success is not getting a huge fine. Saguaros fall under Arizona’s Protected Plants Law. A property owner is allowed to transplant a cactus but must apply for a permit (it’s like getting a hunting tag) through the Arizona Dept. of Agriculture. There is also another permit required for moving the plant off the property. I’m not sure how the oversight works exactly but I believe you have to make sure the saguaro doesn’t die. All that can be learned when you visit the AZ Dept. of Agriculture office.
Now to the complicated process…. a first thing to consider is the enormous weight of the things. Imagine its volume compared to the equivalent of water. So a big one can be multiple thousands of pounds. Think a hundred pounds per foot of height, plus the arms (note that arm distribution will also determine center of gravity). The harsh reality is the bigger the cactus the less likely you’ll succeed due to possibility of failures across all aspects of the process. If the legality and enormity of the cactus works for you then consider this protocol:
Check for disease or damage as high health is essential to survival of the trauma of transplant.
Make sure you have all your materials (and plan) ready such as stabilization/straps/rope, shovels, loppers/saw, padding. Make sure you clean and sanitize the shovel and loppers/saw blade as they will be cutting the roots. Know your planting site ahead of time and make sure it is a good place for saguaros to thrive (i.e. well drained, away from runoff, in general high and dry, also know if utility lines are below). It is best to transplant when night temps are above 60F.
Mark the side facing the sun so you can orient the plant the correct direction. The south side (sunny side) will be tolerant to direct sunlight; the other sides could sunburn if you orient it incorrectly.
You’ll need to figure a way of holding the cactus upright and lifting it up and out. Usually a crane system is rigged up with straps and such, taking care to not rip arms or tear spines and skin off. This is where hiring professionals makes sense. Whatever the case, use old carpet and furniture cushions or something to wrap the saguaro to protect it then secure ropes or straps. Be sure to know the north or south side of the plant so you plant it in the right direction.
Start digging down about a foot out from the base of the saguaro and concave to a foot or so deep. The saguaro has lateral roots near the surface and central, deeper vertical roots. When you get to what looks like a taproot severe it about a foot or so deep. Usually the taproot is shortened to a stub, like 6 inches, since it is pointless to plant it on a long narrowing taproot; it’ll have to make a new one and it is best to start with a stub.
Next you will allow the exposed roots to dry. So, depending on what the set up is, lay the saguaro down on the bed of the truck and let the roots air dry, leaving the severed roots with scabs. Hopefully you can do this on a warm, dry day. From hours to days depending, once it has dried up scabs it is safe to plant, as it won’t have open wounds exposed to soil.
When at the site dig your hole in your well-selected location. It should be a bit bigger than your root ball and a bit deeper (but not too much) than original depth. Make sure the tap root will be able to penetrate down (they grow at most a few feet deep) so break up or remove rocks and hard soil that may make it difficult for the root to dive down.
Place the saguaro the right orientation and make sure it is propped up from all sides. Backfill, tamping the soil every few inches. Then when to grade make a tapered mound around the base to prevent erosion as the soil settles. Saguaros love tipping over after planting so make sure the backfill and propping is done well. Also, don’t plant too deep thinking it will help stabilize it because the lateral roots will not grow out. The norm is to make 2×4 props with carpet at the ends, this seems to be a good way to go as long as the wood is not going to rot and weaken in the next couple years (saguaros grow very slow so they will be unstable for a long time).
Unlike normal transplants, do not water the saguaro in. It has a good store of water. If the soil is dry it will ensure the danger of root rot is minimized. Dried, scabbed root wounds and dry soil help the saguaros natural defenses fend off disease. Ideally, you will never need to water the cactus, but if it shows signs of dehydration after a few months and there’s no rain in sight give it a bit, like a couple quarts.