I've had good luck with Live Aquaria. My daughter not so much. I order marine while she orders freshwater. Having said that the time of your post couldn't have been better because like you I also jumped on the purple tang pricing. Unlike you however mine didn't make it and I have already been credited with a refund. I ordered a small purple and similar to what you showed mine looked the same. Thin and something wrong with the fins. The fins on the top edges, and lower, are clear not purple/yellow.
I'm up North just outside Sacramento living near Mather airfield. LA is down in the Southern part of crazy state so this is one reason why I purchase from them. Less time in the cold, heat, or in transient. Nine out of ten times this works. Boxes have no visible sign of damage. Arrived first thing in the morning. I believe by 0930. I had two shipments. Purple tang and a bunch of snails - you will see why in a second. Anyway I had everything all ready for a freshwater dip using Mr. Fenner's Methylene Blue directions minus a QT tank. I know - another story. But..well, no buts. I know. Anyway on to this purple tang. Turned off lighting. Ambient lighting was also off with window blinds closed. Me, purple tang, and my GSD watching. Observe bag. First thing I noticed is that with my previous tang (Lt. Tang) it arrived in a similar bag but it was blacked out 3/4 of the bag. This bag was clear with lower area white. I can see the tang in the middle moving so slightly but no signs of velvet, ich, damage. Float bag to temp about 15 minutes and get ready for bath.
Fresh water bath time, er, no. Fresh water dip of 5 minutes. The bath process freaks me out more than it does the fish so I use the 5 minute process. Grab stop watch, Netrile gloves on, vent bag, scoop out fish, no struggle, place in bucket, start timer, observe. No signs of lift off, no signs of thrashing, no signs of duress. It just swam around ever so slightly like nothing was wrong. Timer kicked off, scoop out fish, placed into styrofoam box with fresh saltwater at 1.020 specific gravity. I tested the water LA had and it was close so I used mine instead of the bag thinking if a parasite or fluke was in there it would be back on it after the bath. Anyway - that was my logic. Using the drip process I monitored and over 2 hours let the salinity match my tank.
About two hours go by and salinity matches the tang is still sort of in the center and slightly swimming. Figured we are good, new pair of gloves, scoop up purple tang, place into display (I know...). It swims ever so slightly, few laps along the tanks wall, and then to the bottom it goes listing on its side. I let it go for a few minutes not doing anything. New pair of gloves on, ladder, scoop it up, and sort of lightly move it left right to get water through the gills. This worked, it seemed fine, but I decided to start acclimation over again so back in the styrofoam box for a bit with tank water to just isolate and watch. Stopped leaning, started to swim around more, better all around in another hour moved to the display again and it was doing great. This was on Wednesday. Thursday morning I didn't see it at all so feared the worse. My daughter got home from work and looked at the tank and the purple tang was near the sea swirl just hanging out. It later swam all around the tank but didn't eat any nori even though it passed it. I fed pellets, nothing. Mysis, nothing. Brine, nothing. Not a lot just a small sample in addition to the fishes normal feeding. No one cared he was there, he didn't care about the others. Just not much movement. 30 minutes before lights out I noticed he was swimming slow. 10 minutes later it was on its side, flat, no gill or fin movement. Dead.
I can't say what it was, why it died. I can say no flukes - I checked the bucket after the dip. Usually if the fish makes it through the 5 minute freshwater dip then it is strong enough for the rest of its journey. I've done this process with all my fish. Foxface rabbit, Lt. Tang, Azure damsel, coral beauty. All are plump, active, happy, and eat. This guy the only thing I can think of is that it was weak already, then a fire sale, then shipping, then my freshwater dip, then acclimation, then it was too much and done. Maybe if I had a QT I could have just dumped it in and bypassed the FW dip. Maybe. Probably? Can't second guess now. Ironically enough I posted earlier in the week of a Regal Angel at a store that I saw eating well, plump, healthy, and I passed because I didn't have a proper QT. That same store had a purple tang that was only 78 bucks but didn't look that great. Again, I passed.
Since I've had good luck with LA in the past, images of my current fish below, I figured the sale was worthy and let us try it. The Lt. Tang you see below was maybe 3" at best when I purchased it in May of this year. It is now almost 8" and plump to match in girth. The foxface rabbit was thin, much like the purple tang, but managed the dip fine similar to the Lt. Tang, and eats non stop. It was just this purple tang that I've had bad luck. The 2nd part of this shipment was a lot of snails as you can see by the green on my rock in the images. Emerald crabs made it, snails of various types and sizes made it, not a single loss.
Just the purple tang...
TL

R - I like LA and have had good luck. This fire sale with purple tangs? Never again. It was crap. Hope yours makes it while I wait to get a QT in place for the next round in a couple months.