I'm going to bet that you'll want 4000+ to comfortably get the plane in and out. You're going to have a hard time with any cabin class twin that will be comfortable with 3000' at gross. The Aztec and 310 will do it (note: this is assuming a 310 with Colemill or RAM engine upgrades), but given what your family wants, that won't work.
In runway selection, you'll also have to consider what risk factor you want. The previous owner of the 310 I fly now flew it out of a 2700 ft strip for 25 years. Never an issue. Never an engine failure, either, but he did a great job of prepping for the engine failure on every takeoff. You'll probably need yearly sim training in a plane like that anyway, which is a good opportunity to practice V1 cuts, etc.
The way the 310's previous owner used to do it was to put hands on the props as soon as the gear came up. The EGT/TIT becomes part of your scan. If you have an engine failure, you look at the EGT/TIT to determine which one is bad, and feather that engine. Out of a tight strip like that (in his case with obstacles), you do not have the time to do otherwise if you want to clear the trees. He did that at SimCom, they dinged him on it, and the next year were teaching it that way.
I think the Navajo will do short fields better than the 421 will. My instructor flies his out of a 3400 ft strip routinely with heavy loads, and I've seen them do significantly shorter than that. That said, I'd rather have the 421 for a number of reasons.
The twin does offer a lot of safety factor, assuming a proficient and thoughtful pilot. For the relatively light loads you're looking at for a 421, you'd do well. The 414 I think you'd find too anemic for the strips you're looking at, and in the event of an engine failure, you'd be pushing on it hard to keep aloft. I know your family is now used to the Matrix and nothing less will do, but a RAM T310R will offer you a lot of safety fator, short field performance, and still have the luggage room. However, it will be tighter, no doubt.