As you asked for a Linux distribution that is closest to in ideals/philosophy to FreeBSD, there's absolutely no doubt that the distribution would be either Slackware or Debian.
Concerning Slackware, this similarity is exactly the reason why I (as Slackware user) like FreeBSD as well and keep trying to switch to it.
It's very clear that Slackware draws a lot of inspiration from FreeBSD: as mentioned above, the init process is closest to FreeBSD with just one directory for all the startup scripts. Arch and Gentoo are totally different here. Debian is also different, with its SysV runlevels.
Arch has a central config file like FreeBSD has, but this alone does not make for a lot of resemblance to FreeBSD.
Then the overall feel: When you install Slackware, it's almost like installing FreeBSD. Slackware is built around the KISS principle. No fuss. No fancy GUI config tools. Just some simple ncurses-based tools. But only a few. Naturally, FreeBSD is far more complex and heavy (in my view) than Slack, but this may just be because it is a BSD. Any BSD will feel heavier than a Linux distribution. It's hard to describe what I mean by "heavy". To me it's that feeling of an over-whelming complexity. Well, because it's Unix. Linux is simpler, hides more of complex layers. FreeBSD is vaster as you are (rightfully) expected to know your CLI. Linux does the GUI shift, every year a bit more. Which annoys me. At least, that is my impression. BSD is simple more awe-inspiring with all its UNIX heritage. But back to the question:
It's all for stability in Slack - both Gentoo and Arch are not. On the contrary. They believe in bleeding edge. As for Arch, this means that the system is broken by default. At least that's been my experience. Installed it twice, and always the famous PakMan package manager ****ed the system up. Debian of course is very stable, yes, but then Debian differs more from BSD than Slack in many other aspects.
On the other hand, concerning the process of how the system is built/maintained Debian is more similar to FreeBSD than Slackware. Both have a lot of manpower, a lot of policy. And democratic structures. This is part of philosophy, too. Whereas with Slack, manpower is limited, to put it mildly. How they manage to deliver so consistently and with that high level of quality is amazing, given that it is only Pat Volkerding and a bunch of guys. And Slack is not democratic and not open.
Gentoo is BSD-like with its Portage system. Slackware users and Arch users are used to work with build systems, too. In Slackware you have SlackBuilds, which let you compile a very simple tgz file. But the SB mechanism is extremely simple. You cannot easily tweak the build - apart from messing with the script. I have never working with Gentoo, but from a couple of reads, I can say, that Gentoo will be closest to FreeBSD, when it comes to ports. Naturally, as they borrowed the whole concept from FreeBSD.
Conclusion:
You wrote: "I'm looking for organization, stability, security, and reliability, with the smallest amount of closed-source components as possible (preferably none)."
I would NOT recommend Arch or Gentoo to you. Bleeding edge and stability just don't match, impossible. Reliable and stable means either Debian or Slackware.
Concerning security, I really cannot judge. I would guess that both are rather secure. Debian has its own security team. Slack has not, as they are simple not enough people.
You have more packages for Debian than for Slackware. A couple of times more. So if you want a lot of choice and want to make sure you only have FOSS, Debian would be right for you.
Still, I could imagine, that you will like Slackware the most, just because it is so small and simple. It tries hard to remain as close to the UNIX heritage as possible. This is nothing to be taken for granted in Linux. FreeBSD does that, too. More so. Well, try Slack, maybe you like it. I hope so
