First, I'm not a tang-policewoman, but I will suggest that you keep a close eye on the Sohal tang, they're known for having a bit of an evil streak. Calling a tang a "blue" tang could mean many types of tangs, pics or taxonomic descriptions (genus and species) are most helpful if you can supply the information.
No. Antibiotics will not treat the apparent ich (a protozoan), and the only known, effective cures for it are copper or hyposalinity. Needless to say, you don't want to use these in your system with the inverts, as both will no doubt kill them. If the fish are severly infected, I would not waste time with hyposalinity but go directly to copper (be sure you have a good quality test kit for this) to avoid time delays. If the fish aren't very badly infected, then I would first try hyposalinity, unless it appears to stress them further.
It is possible for the infection to clear on its own, but perfect parameters are a must. Unfortunately, unless you're using seawater you simply don't know all the factors that go into "perfect" water, especially since we can't test everything that makes water a quality/NSW (near sea water) product. This is also including the issue of stress--not just from the move but any within or outside of the system. If they seem jumpy at all, they're stressing. Far too many folks understand that stressing certain fish will make them susceptible to these infections, but don't seem to give much thought to long-term stress in the main display.
I'm assuming that since you posted no ammonia oxidation param's that they are at zero readings, and that you are using high quality test kits. However, fish being what they are, I wouldn't count on it clearing on its own. The addition of cleaners (shrimps are my first choice, absolutely no cleaner wrasses, though neon gobies are known and will do well in captivity) will be of a great help, even without these parasites/pathogens apparent. They cannot, however, be relied upon if the fish are severly affected.
The only reliable methods I can recommend to you is to set up a large q/t-hospital system and put the tangs in it ASAP, then treat them with copper per directions. Hyposalinity (less than 1011) is another good, non-drug method. I am going to suggest very strongly that you ALWAYS q/t everything that goes into your main display for reasons such as this. A minimum of 30 days is an absolute requirement in my book. You would then leave the fish in the q/t after the 30 days (in this particular case) and let the tank lie fallow with NO fish for a minimum of 6 weeks.
UV and ozone will not cure the outbreak, they can only help control it, the degree to which they're able to do so is questionable. However, they will also kill the beneficial organisms you'll need for your corals. Running UV in the hospital may be of some benefit, but in my opinion it's not necessary as long as the tank bottom is bare and can be siphoned off daily to remove protozoan cysts.
