You could catch some small beaver, but the one I caught last week, in the pic below. His head barely fit into a 330. The width of the body is about 24" and length nose to tail is 47". A 7" square I don't think would have fit past his ears. If so, you may knock it out and consequently drown it under the ice only to waste a valuable pelt.
The least I would CHOOSE to go with is a 280. Baited under the ice most people say good things about their ability to take beaver in a baited set, as you are not trying to bet them through them, just their head into them. I would not consider a 280 the best choice for a channel, but I have caught beaver in them in channels. Under Ice Beaver in the archives
can explain how to set a bodygrip baited under the ice.
Having read your posts I realize the 220 is what you got and no $ for another trap. So I would set the 220 in a baited hanging set. Catch a couple small beavers, or get lucky on a big one. Use that $ to move into a 330 or a 280. In my opinion, have a safety BEFORE you set one of them; they are unforgiving.
Beaver are pretty easy to catch if not trying to clean out a colony. Even through the ice. Although a lot of work putting them up, it is fairly forgiving of mistakes and therefore has helped me learn. You can also sell beaver "in the green" which means skun, not fleshed. A good way to generate some money for a fleshing knife or other equipment. Groenwold fur gives a good price for green beaver and buys in Wisconsin.
Another option would be to catch a couple muskrats, an otter, or a mink in blind sets with that 220 and buy a 330 or 280. A dam cross over in open water, or under the ice, can produce these. Otter & mink can take a while. A carrot, celery, or apple on the 220 trigger under the ice will earn you muskrats quick if they are in your area, and can pick up "incidental" beaver.
Keep a log of what you do and you will be more efficient in the future.