The bridge pickup looks a long way from the strings. Raising it so that it's about 2mm away on the treble side and 3mm on the bass side should add in a lot more mids and bass, and increase the output.
[Facepalm] thanks for the tip, Simon. I raised it like you said and now it sounds much better. I'll have a crack at doing the bridge and cavity in the next day or two when time permits.