I went DFW>SF a couple weeks ago by car, although in reality I started on the tank move back in January.
In order of most cost to least cost, which happens to almost perfectly match order of least stress to most stress:
1) Sell everything, use it as an excuse to upgrade, get settled, buy stuff there. I don't know how the scene is in Austin, but Dallas has the largest reef club in the country. It's not hard to find frags of just about whatever you want in a store or at a frag swap, which there are at least 8-12 of in a given year. The hobbyist ones are much cheaper, and there are 3-6 of those a year that I can think of off hand.
2) Sell everything live, move the equipment, get settled, buy stuff there.
3) If you have the time, set up a tank at the destination. This could be an upgrade, but it could also be a used tank that meets the bare minimum you can keep your livestock in. Once it's stable go on a nice flight, use a LFS with an air cargo permit (cheaper than you might think), put it on the same flight as you, offload to the new tank. I actually have the permit now and I wish I'd just done this.
4) Move in a Hail Mary. More on this below.
I just did this drive going the other way with my father (DFW>SF) and from the time we started bagging the fish (maybe 30 minutes before departure including arranging them in to the car, etc.) to the time I unloaded them in the tank here was 32 hours. Now, I had a flat tire at midnight Friday an hour east of Lubbock, TX (an hour outside of almost nowhere) that easily cost me 3-4 hours (diagnose, failed plug effort, partially successful sealant effort, sealant effort that lasted several hours, repair at a tire store 2 states later after they opened). The speed limit most of that drive is 75 mph and we were going roughly 80, so driving on the spare wasn't an option even if we did spend 30 minutes digging it out of the trunk. Fortunately we hit no real traffic backups on the drive. My father did need to stop for 10 minutes or so every 2-3 hours, so that added some time. If you're in a moving truck you may not be going 80 MPH.
Where I'm going with this is that while you might do the drive in 26-28 hours you'll also need an hour or two to pack the fish, tear down and pack the tank they are in, and then an hour or two of setup at the destination if they are going back in to the same tank. That can easily put you at 30+ hours if nothing goes wrong, and if you're going to be setting up a reef tank after 30 hours of limited sleep and driving. I did a 16-17 hour move from Indiana to Texas 5 or so years ago. Just carrying the tanks from the truck up the stairs to our temporary apartment was a lot of effort, and the biggest thing I moved then was a 75 (holding the livestock from a 300 that came with the movers).
If you really do want to go with the Hail Mary here is a rough outline you should consider and expand upon:
0) In advance make sure your tank is clean of excess detritus. This includes making sure your sand will pass a drop test, blowing off the rocks, cleaning the corners of the sump, etc. You don't want this to get stirred up any more than it needs to once you start moving things.
1) Make sure *everything* else is packed up in advance. You want to be able to grab the fish, the tank, and go.
2) If you're driving something big enough that the fish and coral can go in a large 55 gallon drum, trash can, etc, you have more leeway. Get that in the truck (VERY well secured), move the fish, put in a battery powered air pump (or two), and strap on the lid. Consider what braking is doing to do to that much water, consider that you want the water to stay inside the container, and consider that you don't want that sloshing 400 pound load to cause issues with handling. Ideally you would have a large inverter also powering heaters if you do this in a cooler time of the year, although as warm as things are now you might need to stop and throw in a bag of ice (inside another trash bag to keep from diluting salinity, you'll be doing this more than once) to cool things. Having this large holding reservoir will buy you a LOT of time if you can keep temperature regulated. You can also do this with 5 gallon buckets, but then you need more air stones, more trouble to maintain temperature, etc.
3) Roughly 12-24 hours before you plan to depart catch all the fish. They need to be moved so that they'll get a bit nervous and relieve themselves. If their first shock is moving in to the bags they're going to be swimming in a lot of fish waste for 24 hours and that won't go well. Get them to relieve themselves in advance of transportation (in new clean water) and things will go much better for you.
4) Also the night before take out anything not critical. Ideally the lights and any non-critical equipment is packed at this point. Even that extra circulation pump on the opposite wall that's nice long term but not needed overnight should be packed. If you're throwing this stuff in cardboard boxes, open and build the boxes, anything that you can do sooner should be done.
5) Once it's go time get the fish into either the big container, bags, whatever. Start a timer. Do the coral first, it's hardier. Euphyllia should be rubber banded to foam (pink insulation foam is safe) so that they float upside down and don't damage the heads/break the bags. Assume the bags will leak and make sure whatever container they are in is also waterproof, at least on the bottom and sides.
6) If you're going to be bagging the fish then have them bagged in large bags with one fish per bag and topped off with oxygen. You can use the passenger cavity A/C to regulate temperature or put them in styrofoam boxes (buy, or see if the LFS has spares to give away). If you're with a large container with air stones then you can obviously skip this step, but now is the time to move them to that container.
7) Move things to the vehicle that aren't already. Hopefully you planned this a bit in advance, this stuff can take more space than you think.
8) Make the drive safely.
9) Unpack and get water in the display, you might as well mix it in the display. Don't worry about the sump, just stop shy of the overflow. You aren't going to want the water they transported in. You did bring 1.5x as much salt as you need with you already right? And dechlor since you don't have time to make RO water? I suppose you could also transport enough water to fill your display in clean jugs, but most people don't have that many jugs. You could try to buy from a LFS, but if something goes wrong like a flat tire and you arrive after the LFS closes you're in a bad spot, so don't plan for that or at least have a backup plan. Once the tank is on the stand, and possibly before, is the point it which you run a risk of this becoming a one person activity. I had a friend that was actually somewhat excited about helping me drive across the country the first time, but neither he nor my wife were willing to carry anything on arrival until they had a 3 hour nap, and that's 3 more hours on the clock. I wasn't really up for doing anything either, but I had no choice as I needed to get the fish out of the truck in the Texas heat. On the latter trip my father helped, but it was a somewhat tense situation after being cooped up that long and I already had the tank running when we arrived.
10) Get the fish in, get the coral in, get some circulation going. Stop the timer.
11) Sleep a bit.
12) Get the rest of the system going.
13) Offer nori.
14) Stack your rocks and either clean your sand and then put it back in, or put in new sand.
15) Thank your helpers.
