I recently went through hypo to treat ich. I was lucky that my tank didn't have much coral in it so I did it in the main tank with the 11 fish.
It would seem very challenging to keep a small tank worth such a large amount of fish alive for the process.
I'll say this: initially I chose to try a management strategy - I bought a 50w uv, fed heavy, etc. One of my blue tangs with started turning for the worse and it would seem he was a few days away from bring overcome and killed. I activated the hypo protocol, which takes a few days to pull down to the level you need to destroy ich. However it didn't take as long to start suppressing it and he recovered quickly enough.
I guess my point is - try management if you like, but be ready to go into treatment as soon as they start taking a turn.
Nothing in life is perfect.
So for management, a more comprehensive strategy is probably required.
Reduce stress for the fish if possible. This one has more meat on it if they are being removed to an observation tank. Most people build that tank like a prison cell (stark, barren, high stress) when it should be like a resort (hiding spots, fake plants, a little live rock, low stress). A reef tank should already be low stress if that's where they'll be....if not, remove the stressors (bullying fish?).
Feeding (more) is not a treatment of course. Hopefully they are already being fed well when the s**t goes down....or that might be considered part of the cause. :)
UV alone might not be sufficient if you want to be really serious about it. UV can kill them, up to 99% effective...but that number becomes less if UV is too weak in power or too strong in flow...either way the UV dosage won't quite cut it to get a 99% kill. (Most people aren't going to be able to verify the kill rate they are actually getting.)
To compensate for those vagaries in UV, combining micron filtration will directly remove swarmers from the water column – dead or alive, doesn't matter. Micron alone is also an option since it's relatively inexpensive you can go bigger with it. Can you add a low-micron filter sock on your drain(s)? There are also self-powered micron filter options like the DIY design
@Paul B has posted about a lot, Marineland's Polishing filters as well as in-line filters like Nu-Clear's canister filters. 25 micron and lower would be an ideal micron range...keeping in mind the lower the number the lower the flowrate will be through the filter and the more stages of pests it will capture. Adding parallel filters can get the tank turnover number where you want it even with very low micron filters.
The UV+micron combination should largely take care of the water column.
For the fish, you can also consider using something like Ruby Reef's additives in addition to feeding them well.
Also, a freshwater dip before the fish goes into the tank the first time isn't a bad idea.