I'd be impressed to see a router actually run a Minecraft server. Every consumer router in the world are very resource limited. The processors on them are puny. Even if you had the ram to run that java file, I highly doubt you could run a reasonable Minecraft server on any consumer grade router.

Those pandaboards look very cool. My main worry is the processor on that pandaboard is not strong enough, but I don't have a good gauge as to how much processing power you need for Minecraft. I can tell you that my server has a dual core 2.4GHz processor, and runs Minecraft just fine.

If you go with one of them, I would highly recommend you get at least 2GB of RAM in one of those if you can, as Minecraft is a memory hungry application on both clients and servers.

Since days of research yielded nothing truly helpful... does anyone think it is possible for me to unsolder the RAM on the PandaBoard ES and replace it with a 2 GB replacement?

Well, a step above the OMAP4430 would be the OMAP4460, which according to Wikipedia, is the PandaBoard ES. But if I got the OMAP4460, wouldn't I have to connect/assemble the components, such as the RAM, myself?

I think I might drop my decision of getting a single-board computer and just getting a very small computer or building a computer without a graphics card.
Also, I might just drop the MC server idea entirely, because wouldn't having the server up in my home take up a lot of bandwidth? According to that chart, my 4 MB upload/20 MB download isn't efficient enough to hold more than ~12 people.

Like I told you, 4 MB upload, 20 MB download.

That was the closest. Here's something a test from me (Chicago, IL) to Los Angeles, CA.

That looks like a pretty good box for your needs. I would also use it as a personal file server as well if you buy it.

As for bandwidth, my server starts running into bandwidth problems when more than 5 players connect to it. My internet is very similar to yours actually, so that'll give you an idea of what you're able to do.

Also, if you start uploading a video while people are in the server, people will complain. 

*trips and finds this on the floor*