Life probably isn't good for clown stuck in 3 gallons of water. The dwarf seahorse isn't a bad choice, but they are annoying to feed. Dwarf seahorses move very little, but arn't really worth the trouble of hatching brine shrimp every day IMO.
Saying any type of goby would be workable is simply not true. Mandarins are gobies, engineer gobies get over a foot long, diamond gobies get to be 5", court jesters need a supply of pods although less than a mandarin, nearly every goby out there is going to live a very short life in a 3 gallon tank.
There are a very small handful of gobies that "might" be workable in a 3 gallon. Some clown gobies, Catalinas(if you can keep them cold), Red-headed gobies, and I think Trimma gobies might stay small enough. Even those would be hard to keep I'd think. My 3 gallon tank shifts a lot in water chemistry from one day to the next.
A successful tank isn't one that was pretty at the pet shop. It is one that can sustain the livestock in it comfortably. You can put anything you want in a 3 gallon. You are just condemning it to a short and unpleasant life if it isn't appropriate. So if you plan to just replace the losses at least buy tank bred fish. That way you aren't wasting wild caught fish.