First thing I would do would be to transfer them to the hospital tank with new water and same temperature, after first doing the 12 minute FW dip. Slowly drop the temperature to 68° so that whatever is affecting them at least won't make it worse by having a bacterial infestation.
I don't know that anyone can tell for sure the exact cause of the rapid respiration but in my case I do a fresh water dip for 12 minutes to see if parasites are evident.
If the seahorses thrash around when placed in the fresh water, it is usually a sign of parasites exiting from wherever and often you can see them in the water if you look close enough.
The dip is done at the same pH and temperature of the water they come from, and are left for 12 minutes, unless they become unresponsive to touching them.
Unfortunately I have had some that didn't show parasites and I didn't know what to treat for so next time if they don't show parasites, and don't have any sign of bacterial problem, I'm going to assume an internal problem and treat with diamox and see what happens.