Just because the regal angel isn't showing outward signs of ich doesn't mean it isn't bothered by parasites. Existing fish often develop an "immunity" to ich and are rarely overwhelmed by it. OTOH, the stress factor in new fish leaves them susceptible to ich. If the problem was bacterial, you'd see cloudy areas on the fins and body, especially on the pectoral fins. There's probably little you can do short of treating the fish in a separate aquarium, and that may be too late now. Sorry to be so pessimistic, but these are delicate fish and we should never be cavalier about their care.
BTW, you didn't list measurements fo pH and alkalinity, which are important parameters.