I finally finished Final Fantasy VIII!
I had saved the game just before the final battle, but had never prevailed--and since I'd usually played at night, I got only one chance per session. This afternoon, though, I tweaked my characters' abilities and played it through. The battle took almost two hours, and I was rewarded with nearly 20 minutes of video, including the closing credits (which are well worth staying through).
Unfortunately, the game simply stopped after that...it offered no save point or way of accessing the in-game video again short of playing through once more. Which, of course, I will do--I learned a lot in the ten months I spent playing the game (in brief installments) and would like to begin the game again with the understanding of its mechanisms I have now.