Which criteria provides the most stability at sea in a 48-55 foot?

First what speeds and distances are you looking to make? Everything is a trade off. You can have very small vessel that's a lot more stable than a much larger one.

Hull design and how well the builder got the COG and weight to match the hull design..........and location of weight......stabilization....... A great hull doesn't need stabilization, no amount of stabilization will fix a bad hull.

For what you describe I'd stick with the Vikings from that list. They'll give you the speed, range. and decent fuel burn. You won't need to stabilize them, and you can drop a line off the back to catch dinner. If you find you need more interior or entertaining space or something more sedate there's a lot of choices, but I get the feeling a SF is what will appeal to you most right now. Some boats need stabilizers, but mostly the FBMYs or trawler styles. Once you get speed going they mostly just get in the way unless you go for a gyrostabilizer.

Btw, for that occasional extra long trips you can always throw some barrels of fuel or a bladder tank into your cockpit.

In that case look at the Viking SC (Princess). I used to run a 2002 50'. Classy, well built boat and I had her in all sorts of weather. The lower helm is also a wonderful thing when the weather goes bad or the seas kick up.

I would absolutely look at the 52' Searay SB over a Carver, Searays are fine 2000 or newer and a pretty well built Boat and I'd put it in front of Viking SC for several reasons. Neptunus is also a well built boat and I'd put that over Vking SC as well. SF will get you what you want in that size easily and I would not overlook them and they're a better sea boat generally. Looking at fuel tankage is completely meaningless, it all depends on your actual range at 80% fuel capacity (tankage and efficiency). Princess are ok, but gelcoat fares below Searay (which had amazing gelcoat in that era), access to the engines completely sucks, and teak decks are going to need replacing if they haven't already.......In that era and size I'd also look at Sunseeker and put them slightly above Princess.

However beam, deadrise, keel, weight, etc. can make stabilizers unnecessary, and not worth the cost.

1/3 more. Yes, especially when docking. Possibly mean slower and/or more fuel burn also.

I disagree with this. At cruise speed on a very good planing hull, stabilizers add very little to stability because the boat is so stable to begin with. I can name several, even ones that are stabilized that ride worse with the stabilizers on. I don't care what stabilizers you add to a very unstable, top heavy boat, yes it will ride better, but never as good as a good hull to begin with. It's a band aid, so to speak. This is one area where some of the Euro builders excel at over the American builders, and why you see it a rarer event for a Euro motoryacht that cruises over 25 knots have stabilizers. I run a 62' Predator for a long time, it is an excellent sea boat, stabilizers would add very little at cruise. I ran a new Hatteras 59' GT in a 5' sea off of the starboard bow, at 35 knots it rode horrible with the seakeeper on, it pounded. I locked the seakeeper and it allowed the hull to wiggle just that little bit that it rode great over the waves with no pounding whatsoever. On the 25+ knot cruise boats, the zipwake and Humphrees (trim tabs) actually do a much better job than stabilizers at keeping the boat stable. Now slow down to hull speed and below or stopped and the seakeepers really shine. But I've found the curved fin sidepower stabilizers to be amazing at every aspect and even better than a seakeeper at anchor on a 66' Sunseeker Manhattan (FBMY) with a 27 knot cruise.

No, the 66' Manhattan has a lot of weight up high and is not inherently stable like the predators are. It NEEDS stabilizers and is why they come standard on the vessel.