The lasers are behaving well, there is no high noise or wandering lines. The spectrum below is taken in air: that explains the excess of noise in the few kHz region.
Today I swapped out the 8mW laser and installed two 2.5 mW lasers. I rebuilt the input part of the optical levers and re-aligned everything. See below for a picture of the new setup: red beams are input, yellow beams are output. I also installed a protective screen all around the table, to abvoid any suprios beam to get out.