Don't have a 3" N frame, but do have a 2.75" L Frame M69 5 shot .44 mag. Have shot it a fair amount from up close and personal out to 440 yds. I'm not the best shot, so the 440 yd gong wasn't in much jeopardy -- 50 yards and in, it's a different story.
Was at the range yesterday verifying sight settings on some 22s getting. It was windy and hands were getting really cold, so only shot two rounds with the 2.75" M69 with Federal 240gr JHP (No. 44A) at 50 yards rested. Both hit within 2" of my point of aim from a rest.
One of the locals (above average shooter) showed up to chat and I offered up the little .44 and the remaining box of .44 mags to get his impression. First up was a gas cylinder (one of the tall skinny ones) at 300 yds. He was standing upright with his butt resting on one of the bench rest tables. I was watching thru my binoculars. His first shot was about two feet left of the cylinder but dead on elevation wise -- remember this was the first time he ever touched this gun. He shot the next 10 rounds without hitting the cylinder but wasn't missing by much. He moved in to an 8" swinger at 200 yds for the last 4 rounds. Never hit it, but was much closer -- from my vantage point thru the binoculars, he wasn't more than a foot off the plate in any direction -- almost nailed it with the last shot.
Gun is equipped with Hogue 500 X Frame grips and recoil is "stout" according to my friend but certainly doable. I have around 1,200 rounds (too lazy to look up actual count) thru the gun, most of which (90% .44 Mags). I don't find the recoil objectionable and never noticed the muzzle flash (I mostly use A2400 and H110 in my .44 Mag Loads)
Point being, these short barreled magnums can be very useful and tons of fun and aren't limited to short ranges. Yes, you'll give up some ballistic advantage to longer barrels (and sight radius), but I wouldn't hesitate to take a shot at an elk within 50 yds. FWIW, I've chronoed some 315gr and 325gr Cast FN GCs right at 1,100 fps. My preferred load is an LBT 260gr WFNGC at a bit over 1,100 fps which also happens to be the guns favorite load.
50 yard target rested on my range bag (verified on a differnt day).
Here's a picture with a set of Hogues 500s that I modified a bit.
Paul