A 2 3/4" shotgun will most certainly do the job...even with steel shot...as long as you do your job of putting the pattern on the bird!
When steel shot use became law in Canada there was absolutely nothing wrong with it. I would even go so far as to say steel shot was better back then than it is today! The problem was that people used the wrong shot sizes (too big just as often as too small) and didn't pattern their guns at the distances they expected to be shooting waterfowl at or any distance for that matter!!! The smaller sizes crippled birds because of a lack of penetration and the larger ones (BBB, T, TT, F) did the same because of a lack of pattern density! That is where the big push for longer chambers came from. However, even in the 3" and 3.5" 12ga. and the 10ga. guns, the larger pellet sizes still didn't give you the pattern density required to make clean kills beyond 45yds. Fast forward 10 years and the "speed kills" craze hits the shotgunning world! The problem is that hi-speed loads don't pattern very well at longer ranges (some don't even make the cut at 30 yds) and payloads are reduced to make the speeds possible. To make matters worse the best shot size, #1, is damned near impossible to find.
For the last 14 years my go to load has been the factory Federal 2 3/4", 1 1/4oz, #1 steel shot @ 1275fps shotshell. Fortunately, I stocked up years ago because it is no longer produced. With that load I have knocked birds down as far as 62yds!
Whether I'm using lead, steel, bismuth, tungsten-iron, tungsten-matrix...I have yet to notice any difference in killing efficiency when the bird is centered in...or missed with a pattern that is shot using a 2 3/4", 3" or 3.5" 12ga load or even a 10ga 3.5" load!