IF you can get them to live...the so-called TR kelloggi, which actually appear to be hybrids, have a dismal survival rate, even in the hands of very experienced keepers. Check the adult size of H. kelloggi...we're talking a 12" SH. I've kept SH in 18T's (20 XT), and I can tell you that even a pair of H. erectus or H. reidi are a pretty tight fit.
As mentioned, you'll want to keep the tank cooler...74*F max for tropicals. SH are very prone to bacterial infections, and in captive systems above 75*F, the bacterial count starts to get very high, esp. in a small system.
You'd do better to go with smaller TRUE CB SH species (erectus or reidi) from a reputable breeder such as Seahorse Source or Peka's Ponies. The LFS SH might be cheaper, but there's a cost of ownership that tends to make them MORE expensive (they may need to be weaned to frozen, they'll need prophylactic treatments in QT, and meds if they get sick...then if they die, you're out your $20-something).
As for seeing SH in a smaller tank that were doing fine...did you ask them if they're feeling cramped? My 12"+ adult volitans could probably live in a 20 gal, but it wouldn't be the best thing for it. IME, SH will use every bit of space they're given, esp. lateral space. The extra vertical space you mention typically comes into play when they mate.
As for tankmates...nothing that stings, pinches, will outcompete them for food, fast swimmers, or boisterous fish.
HTH