A quick update, in case anyone has any ideas:
I just did a datalog, every second or so, for about 30,000 records. With the TSL2561 and the code above I'm getting strange results. I'd say more than 99% of the time I'm getting consistent results, but I am getting strange spikes (to zero and to high values) that I can't explain.
I'm measuring the light outside of my window. Last night (very dark) it's very consistent, with no spikes. However, as more light falls on the sensor, there are more spikes. Also, it looks like there are periods where the light drops to moderate levels, with occasional spikes to the expected levels.
I'm going to work on building a new sensor pod for monitoring in the house with a very consistent light source. I'll post up with any findings.