My update is:
Continued working on ViewTopicList.
I finished writing the tests, and they are all passing locally when just that class is run.
However, they don't on Jenkins, so I'm working on that. I've built PHP 5.3.29 from source (as close as I could find to 5.3.10, which Jenkins runs), and I'm trying to also use Jenkins' version, 3.7.37, or close enough.
I also realized that I didn't try running the full test suite locally, so that might be the problem. I'll do that today.
Matt