Update:
Made a couple of changes to the original schematic:
- Decreased the supply voltage (BEC output) to 5.8v instead of the 6.14v I was running, which results in less wasted heat.
- Reduced R2 from 10k to 6.8k ohms.
- Added another thermistor (R9) to the PCB to track changes in the enclosure's ambient temperature.
- Used a slightly larger (and prettier) heatsink, and added some cooling holes to the enclosure. I found the BEC was getting a little too warm for my liking since it was not getting any air.
Other than that, the charger seems to be working swimmingly.