My first mistake was the way I threaded it. I miscounted the number of threads in each color block, and then I sleyed the reed entirely wrong - instead of alternating light-dark (or vice-versa) in the slot and holes, I grouped the colors together by two (one slot and one hole both the same color) which gave me a lovely houndstooth-style cloth. So, lovely, but not the original aim. I decided to completely re-sley the reed to try and get the pattern I had hoped. Success! Except that the back of the reed looked like this:
Because I had to rearrange the threads at the back, pulling some out of the warp and tying them together, a few of the remaining warp threads did not get caught around the back beam. Which was fine until I got near the end, and they grew so loose I could not get the yarn to lay smooth when I beat it down. In the end, I opted to cut it off and tag it as a learning experience.
Here's the finished piece, which is less of a table runner and more of an oversized placemat: