IMO Cold water fish are a PITA. They tend to grow big, they produce lots of waste and you tend to be limited on your selection of fish. However if they're you're thing I wouldn't try and change that for the world.
At the moment, Stan is in a body of water that will have a constantly rising level of Ammonia. If the bowl you have him in is unfiltered, the only thing that will reduce the ammonia levels are your water changes. If you move him into the tank, you will still need to do water changes (as you don't have a functioning biological filter), but the ammonia will be far more diluted and it will be easier to keep it to an acceptable level. As a bonus, as you are going through the process of fish-in cycling, your filter will be slowly maturing.
Keeping him in the bowl has very few benefits. The only one I can see is, it's easier to do a full water change on a bowl than a 50-75% one on a larger tank.