All American guns with 32" barrels are much heavier than your P-gun. Yes you can get a lighter weight 32" gun if you look, but all the 21's, 3200's and with few exceptions all the American made 32" doubles are barrel heavy. Not a bad thing if you like a heavy barrel.
Skeet guns get even more barrel heavy when you put tubes in them to shoot small gauges. Makes it much easier to have a smooth swing if it takes a lot of effort to stop the gun. Light weight guns are easy to get moving but hard to swing smoothly, heavy ones are harder to start moving but easier to keep swinging once you get them going. Most clay target games are improved by follow through and heavy barrels give you tons of follow through.
"Game" guns are not 32" heavy barreled guns as a rule unless you count water fowl guns and pigeons guns. You will not see many 32" guns quail hunting, maybe a few dove hunting. Target guns, clay target guns, are almost always heavy by shooters choice. They like the smooth swing and the reduction in felt recoil because of the heavy gun. Most would do just as well if you made the same gun with a set of 30" heavy barrels. Clay target games, which were invented to mimic wild bird shots have evolved into very static games with little game shot relavence. Gone are the low gun, multiple styles of shooting. Todays clay target shooter groove their swing and heavy barrels help.
The longer sighting plane is just a myth. Stack the middle bead and front bead into a figure eight and tell me if it matters if they are 13", 14", 15", 16" or 18" apart. The sight pitcure is the same. NO rib between them, they are stacked. No difference due to the longer sighting plane.
Myths sell guns just like facts. Todays myth is longer is better. The 25" barrel myth sold thousands og guns for a certain British gun maker. The 28 gauge is the perfect or square load has sold thousands of 28's. Just like tighter bores shooting harder or longer barrels killing birds better at long range. Good sellers PR, which sells gun today is longer is better. Message to shooter buy another longer gun and you will do better just because it is longer.
I have started buying some of those 25 and 26" barreled guns that no one likes. They are dirt cheap. 20-30 years ago I bought 16 gauges because they were dead. Bought them for almost nothing. I still have several 16 Foxes that I paid less than $350.00 because they were dead. I bet in 30 years more than a few people will be shooting short barrels. Remember how many 30" and 32" double were bobbed because they were too long. What goes around comes around.