The 421C wingspan is the same as the 414A. So if you can't fit a 414A, you can't fit a 421C.
The shortest I've flown this 414 into so far has been 3,500 ft with a takeoff at gross weight, it did fine. We were going to fly it into Gaston's last year (3,300 ft grass with the trees) and weren't too worried about it, either. If you're based at 3,200 ft it's doable, but you don't have a lot of margin and you won't have accelerate-stop distance if you have to abort the takeoff at a bad time or botch up your landing. Yes, an AoA is a good idea if you're going to do short field landings, and I would get one if I was going to do them routinely with the plane.
The 414 is the worst runway hog of the three (340, 414, 421). The 340 has the same engines and props with a smaller fuselage and less weight. One of my friends specifically chose a 340 over a 414 because he wanted better short field performance and didn't need the space of the 414. If you were considering a Duke and its cabin was acceptable to you, the 340 cabin will be just fine. However now flying a 414, I wouldn't want the smaller cabin. The 340 is a bit faster, but not a lot. MT props help takeoff.
The 421 is going to have the best performance for the same load, but the problem I have with the 421s is that the engines seem to have the highest rates of failures on takeoff. Even though the 421 would've been a better fit for what we do in a lot of ways, I decided the direct drive engines were a better idea. A friend of mine bought a 421B project at the same time we got the 414 project. We've both had our share of problems. Both of us had leaking props in short order. I handled it by getting MT props (which are a huge improvement on the 414), he's planning to do a reseal (way cheaper). We both have had fuel system issues. He had a heater issue (I haven't had one yet). I had a bad fuel selector. His reason for going 421 was because he wanted the larger cabin and the better takeoff performance from short runways. I'm trying to do everything I can to optimize the OEI performance of the 414.
The critical dimension with these planes is typically the back of the tip tanks to the tip of the nose. In my case, a 421B wouldn't fit in my hangar, but the 414 does.
414 does better in ice than the 340 as its wing is fatter. The systems are otherwise basically the same. I'm a fan of the alcohol windshield over the heated personally, but if FIKI is a big deal for you vs. non-FIKI de-ice, then you'll need a later model with the electric windshield. They offered it in '77 (the year of the 414 I fly) but this one has an alcohol windshield.