After some help with what I should do with this plant, I've neglected to check its roots of for some time. I believe it to be a species of asparagus grass, though if someone wants to correct that belief feel free.
As you can see from the images, I may have left the roots alone for too long (in fact I had to literally cut the old plant pot away from the bottom of it, because they'd grown through and formed a circle underneath it The plant itself seems to be fine (in-fact flowered for the first time in the 6-ish years I've had it, though they were very small, and dropped off at the slightest touch).
Is the answer to the question "How do I prune the roots of a rootbound plant?" still appropriate with such a root-locked plant? What's the next size up pot to put it in? It was in a 6' (I think, the next up is a 7' at any rate) pot.