BTW the main band of concern here is 40m. Maybe I could
build a BPF? Anyone know where I could find plans for one?

The noise is arriving in the 40M band. Since a 40M BPF passes 40M, how
wouold it "know" the difference between noise and signal?
As for noise floor- take Pete's suggestion or take your K2 to your friends
house and compare signals there.

It is likely the noise comes from your house- switching power supplies in
consumer electronics, fan speed controls, dimmers, microwave ovens etc.

Put the K2 on battery power and turn offf the main breaker into the house.

Dale W4OP