Boba their skin condition doesn't sound good to me. Does it look like they are experiencing labored breathing?
![Frown :( :(](https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f641.png)
They might have ick or other parasite. I've read that they are also very sensitive to copper so if you ever used that in your system or were planning on medicating the frogfish be certain to avoid that. Check the tank's temperature also.
I suggest making a clean batch of saltwater and putting them in their own tank with an airstone and a few rocks for awhile, as soon as possible. (I'd pre-clean that tank with really hot water and/or vinegar first and flush it completely away, and wipe it out). I did that with my frogfish once when he wasn't looking so good and it perked him right up. High oxygen conent and very clean tank. He's actually still in that tank now, a 20long and is very happy.
Be careful transferring the frogfish betw tanks since you really shouldn't expose them to air or even the surface of a water container as they could ingest an air bubble. Anything they might be infected with will make the trip with them anyway so moving some of the existing tanks water along with them to the hospital tank prob won't make much difference anyway.
When I put him back into his 20high its going to go barebottom this time, and have an air stone for extra oxygen content. Its also going to be in the sump room where its cooler , but facing out into the main room (I installed a 'portable' floor AC unit in there which blows its exhaust outside of the house so its much cooler). When I had the 20h tank setup on a bookcase it would easily overheat, and probably related to the heat get mild cyano outbreaks. I had two remora hang on skimmers and one or two small powerheads in the tank with a few normal aquarium lights and the tank would get so hot that I had to shut off a powerhead and a skimmer.
I still might run into heat vs skimmer and powerhead issues so in the long run I may get a plumbed tank to integrate into the reef circulation system like you had been doing, so that the frogfish tank can share the filtration and temperature conditions of the main system. Of course then the tanks have potential to share any other problems like parasites and other nuisances/outbreaks.