So now armed with the knowledge that the Portable probably maybe kinda works, I did what anyone would in my situation would, I set about Googling the snot out of the problem.

I came across two major sources of information about the problem and potential solutions:

1. Vintage Computer Forums
   1. There were several threads about the issue, which is apparently a widely known one. (Good! I probably have a known problem rather than something more exotic!) However the forums weren't especially helpful in actually resolving the problem, but rather the information was mixed in a mish-mash of guesswork, vague solutions, and anecdotes of other's half-formed solutions. Apparently at one point a guy was selling replacement parts, but people weren't recommending him anymore.
2. Old, Broken Junk
   1. Philip has an excellent website, and he had gone through a similar situation as I with his Compaq Portable. That whole project was covered in a Hackaday retro post back in 2014. Thankfully I didn't have to do quite so much resurrection as he did. About halfway through his post he describes the problems he had with the keyboard.

Ultimately both sources brought me to this conclusion:

There are some little plastic-foam-foil disks in the keyboard that act as the keyboard's contact switches, and they have more than likely self-destucted over the years. They would need to be replaced.