Wow, so I cannot believe I am saying this, but that is a LOT of high bio load fish.
That being said, I keep several large angelfish together without aggression:
My 180 (Angel Tank) has: 4.5" Queen, 4.75" Emperor, 5" Passer, 4.25" Blueface, 4" Rock Beauty, 3.75" Regal Angel, and a 3" Potters Angel. They're all being treated in cupramine, and eventually the Regal Angel will be moved to a different tank.
That same 180 also has: 4" Magnificent Foxface, 4" Moorish Idol, 3.5" Chevron Tang, 2.5" Yellow Belly Hippo Tang, 3" Red Coris Wrasse, 2" Cleaner Wrasse, 2" Maroon Clownfish, 3" Lime Green Wrasse, 3" Sand Sifting Goby. It's pretty heavily stocked. That being said, I am skimming for 450 gallons, have a huge turf scrubber, and do water changes 3-4x per week (until treatment is up and then I suspect I will still need to run 2 35-40 gallon WC per week because of the bio load).
Clown trigger can randomly become aggressive and kill tank inhabitants. With fragile fish like Regal angels, powder blue, and others... I would not do them at all. In fact, they can kill all of those fish overnight if they decide they want to go on their famous murdering streak.
Here is my recommendation of overstocking your tank: Pick 3 Angels and 3 Tangs. Do this because it will spread aggression. Get one foxface. Puffer are SO heavy on the bio load and so too are lionfish, it would cause immense issues, IMO. I would avoid both. Trigger are also very very high in bio load.
SOMETHING has to give. I consider a puffer as bad as two 5" tangs or two 5" angels with bio load, and lionfish about the same.
I would do:
Queen Angel, Regal Angel (very difficult so I would add at same time), and another angel. (add all three within a few days of each other or all at once)
Powder blue, purple, and pick another tang. Naso grow ENORMOUS and I would advise against it with your already high bio load. Just my .02
Magnificent foxface (so beautiful)
Pick two: Eel, lionfish, puffer, trigger
Add an aggressive wrasse or two.
Avoid clown trigger like the plague.
This would be very very highly strocked.
OK now hear me out on the introduction process: Remove a significant portion of your live rock (or buy some dead rock). Add the tangs/angels at about the same time. Get the ammonia badge from seachem. Treat them in cupramine in your display. Keep inverts and some live rock in a rubbermade bin to add back after treatment. Your powder blue tang and regal angel are very fragile and will likely not make it in a system without quarantining. I used to quarantine zero, FYI and had decent success but with what you're attempting there is a 0 percent chance of success. Ramp cupramine up to .5-.6 GRADUALLY (testing daily because of absorption) over one week. Once the amount of cupramine absorbed throughout the day and overnight is zero (no swings in your morning test), and cupramine is steady at .5+, wait four weeks.
Change water (and replace cupramine as you do) every other day. Watch the ammonia badge. Never let it get green. Angels (especially Regal angels) have zero tolerance for ammonia. I would take a piece of media (spongy absorbant type media) from someones existing reef tank to aid the beneficial bacteria and support your bio load.
After four weeks of no signs of distress, remove cupramine with cuprasorb and carbon. It takes 7-10 days for this to occur in a display tank IME. Once the test shows 0 copper, add more carbon and a new back of cuprasorb for 2-3 more days, then add back the live rock and any other "inverts" you dare keep with your stock list (some cheap corals work fine IME).
Add trigger next. They need 4-5 weeks of the same treatment of cupramine in the same process, or CP or another treatment. Do not trust hypo, IMO IME.
After that period, introduce it. Then, add the rest in to qt assuming you don't have nitrite present in the system at all. If you do at any stage, do not add fish until this has stabilized for at least a couple weeks. If you have nitrite or ammonia present, it means you are effectively still cycling. This is not good for your fish. Do not add more.
Add nothing that has not been treated for ich in some effective manner for at least four weeks in a separate quarantine/hospital tank.
Invest in a HEAVY DUTY protein skimmer and other means of filtration. My ASM G4X is rated for 450 gallons. The G5 is as well I believe. It has a large footprint but you will need the extra skimming power. Do 30-40 gallon water changes weekly as well.
I may catch some flack for this but I overstock all of my fish tanks pretty effectively.
I say add the angels and tangs first because they're the most likely to have parasites. Angels come with ich, flukes, and velvet FREQUENTLY. They are also VERY intolerant of these parasites (especially flukes and velvet). The tangs (except the powder blue) can adapt to ich, but not flukes or velvet. You will want to run prazi-pro after completion of your cupramine period as well.
That way, your most fragile fish are treated, your tank has no parasites, and your new additions won't have them either. You won't have to keep the tangs and angels in tiny, unnatural-appearing quarantine quarters which will help with eating and stress (because they're in your DT), and that will help with aggression immensely.
