Some amount of noise is to be expected. It is, after all, a simple high-gain circuit with nothing even resembling noise reduction. That makes the lead dress all the more important. Here are a few things I do with such builds:
* Make sure leads are as short as possible, but not straight-line taut. That really taught wiring is neat looking, but breaks easily when a nut slips and a jack or switch twists.
* Keep input and output wiring well separated. Generally not a problem on BYOC boards wired per directions.
* Avoid twisting wiring (except the battery cable). Like twisted pair network cable, twisting may, in the right circumstances, help reject some noise. Used arbitrarily on any old pair or trio of wires, it can do the opposite.
* When all else fails, use shielded wiring from input jack to switch and to board, and from board to switch to output jack. I've never needed this on a BYOC PCB-based Large Beaver, but have used it on other high-gain builds.
I use vintage single coils (not the noiseless kind) quite a lot with muff-type pedals, so I'm used to some noise from the pickups themselves. I do get a marked increase in noise running the effect near maximum, but the difference between the noise and normal playing volume is pretty substantial, so it really only bothers me when I'm not playing (at which point I just roll the volume to zero on the guitar). If you noise is considerably more than this, I'd say you probably have an opportunity to clean things up and reduce the noise a bit.