I've moved a couple tanks home (Pullman to Issaquah) and here are some thoughts based on those experiences.
First off I would only consider filling those buckets up all the way if you have a truck otherwise you are going to have saltwater soaked carpet
. Even in a truck I would fill them about 70% at the max, they'll still slosh, but it is a bit more manageable.
Also if you have not done a move before, the tank takes up A LOT more space broken down in a car than it does when it is up and running. I know that seems like common sense but it always surprises me how much real estate aquariums take up in cars (it's because you really cannot stack things on them). I hope you don't have to move furniture home this trip.
Two years ago when I moved my 29 gallon home I left the substrate, fish and rocks with corals attached in the tank. I drained down to a couple inches to carry it out to the car then filled it back up about 1/4 the way or so, however much was needed cover the rocks and such. If you have a truck make sure you keep the fish and corals inside the cab.
Last year when I moved my 55 gallon home I took the fish and rocks out but kept the substrate in with some water. It worked better because I wasn't planning on setting up my 55g at home again, also my 55 gallon is drilled and has a closed loop on it so it had more potential to leak, etc.
If it is manageable I feel like it is easier to keep some water in the tank with the fish and corals. It depends on the situation but it's less time to bag things up, chase fish around/etc. But you'll probably need to pump some water in and out of the tank between loading, driving, and unloading. Also a 72g is considerably bigger than a 29g so it's a judgment call you'll have to make.
If you pack the fish and corals separately, which will probably be a better choice in this situation, it helps to make them the last things you take out of the tank. If you use a Styrofoam container make sure you line it with plastic bags. With the 55g I just filled them up directly with water and put rocks in them and the water will slowly seep through the styrofoam. Luckily I had a rubber mat under it. It won't be enough to danger your livestock but you really don't want saltwater in/under the carpet of your car. (I didn't put much thought into it because it was liverock, once you start breaking down the tank the clock is on). That said, make sure you are packed and ready to go so that all you have to do is break down the fish tank and hit the road.
Not to step on any ones toes but I would keep the sand. I understand getting rid of it because of detritus but it is not going to be a problem. These tanks are pretty resilient in my experience, much more so than a college students budget
Run some polyfil in your filters to help clear it up. If you don't have any other form of mechanical filtration run it in your refugium for a day.
If at all possible have someone at home mix up more than enough water because you will be short when you get home. With my 29g I brought back all the extra water from the tank in 1 gallon jugs, its a waste of space and weight if you don't have to and with a 72 gallon, it's just not going to happen. If they don't have a heater that is ok, a gallon jug full of hot water has decent heat transfer properties to bring 60* water up to 77* (whatever you keep your tank at, or higher to help heat the water that's been sitting in the car) pretty quickly. You just want to have it mixed in advanced so you aren't mixing new water and trying to get the tank up at the same time.
Also by having more than enough water at home you can vacuum out the substrate in Pullman. Vacuum it last, after all the fish and corals are out. You also might want to fill up the buckets for the live rock and bags for the fish and corals before removing the live rock to prevent detritus getting in the bags. (fill up the bags, remove the live rock, scoop out the fish/corals and pack them, vacuum the substrate while removing the rest of the water out of the tank).
Just drive straight through, don't waste time stopping to open the bags for oxygen, they will be fine. I have an AC/DC inverter and I never bothered with the heaters/airstones/etc. Keep them in a styrofoam box and fill any extra space in the box with bags of tank water (or tap water that is a couple degrees warmer).
The whole system is going to cool off by a couple degrees, and it is going to take some time for it to warm up. It's not ideal but nothing about moving a tank is. The live stock will be fine. Keeping your fish at 77* while the rest of the water gets down the 75*, then trying to acclimate the fish into colder water, while then shortly after bringing the water back up to 77* is going to shock the fish more. Two summers ago I installed a chiller on my 10 gallon tank here in Pullman and somehow managed to set the temperature to 66* instead of 76*. The tank went from 78* down to 66*, it scared the crap out of me but in the end my clowns and corals all survived. This happened over a 6-7 hour period of time (my second mistake was freaking out about the 66* and trying to get the temp back up to 76* I didn't realize that raising the temp too quickly would also stress the fish). I remember seeing the chiller read 66* and thought "no way, that's wrong" then stuck my finger in the tank and it was not wrong! At the other end of the spectrum I had a heater short out and fry my picotope at the beginning of this semester. The temp was 88*F when I got home. I only had hermits, snails and soft corals in it, I lost the snails almost instantly and a couple hermits, the corals weren't too happy until a couple water changes later, but a lot more survived than I imagined, and that was with the heater cracked in half, arcing under water.
I would pass on the heaters and focus on using your time efficiently. If you are worried about it I would use heat packs instead, less risky and less time consuming. Again keep in mind if your fish are in water that is a few degrees warmer than the rest of the water you aren't really doing them any favors, instead of having a 6 hour drive to acclimate, they'll have a 45-75 minute drip acclimation to the lower temperature, then a couple hours back up as the heater brings the tank back up.
If you need a styrofoam container I have one you can have. It's pretty nice (a lot better than the safeway ones) and it's sitting inside a cardboard box. (it's from a saltwaterfish.com order).
If you are heading out on thursday or friday I should have some (a lot of) free time if you want an extra pair of hands to help. I know how much of a PITA it is to do alone.
Sorry for the novel, hopefully it helps!