I would make a simple jig and use a standard straight router bit. adjustable to any sized/height box with the exception that you might want to size it to an exact number of finger.
My main hobby is restoring domestic vintage valve radios for which items of test equipment is called for. I and others in the hobby design and build simple items of test equipment to meet our needs and for many years, I've made little comb-jointed ('AKA finger join, box joint') from offcuts of mahogany and oak 1/4" thick using a home-made router jig which cost me nothing. The boxes cost me nothing and look a bit 'retro' like 'crystal set' boxes of yesteryear, so are in keeping with the hobby. I use a router bought from a car boot sale for a tenner, and a 1/4" straight sided router bit, but other sized bits and wood thicknesses could be used if desired. In use, the jig is held in place with a batten along the underside of the front edge, in a woodworking vice attached to my bench.
The largest box I've made has been 15cms deep x 20cms long, though The jig will make boxes of any length and depth, but my bandsaw will only cut wood up to 15cms depth, which is adequate for my needs. I made the jig to be slightly adjustable to set it so that the joints can be accurately cut for the 'combs' to mesh together. I've found that unless a piece of sacrificial hardboard is placed behind the wood being routed in the jig, some breakout occurs on the rear of the workpiece.
The jig design was from a book 'Making Router Jigs and Gadgets' by the late Roy Sutton.
Some examples below of boxes I've made to house items of home-made electronic test equipment, and of the jig, which broadly consists of a table for the router and a 'sled' which slides in a groove routed in the table. The last pic is of a test piece to check that the jig is accurately set up. (That would be glued up and sanded off at the corner to check that there are no gaps in the joint). Once the first cut has been made, that is located on a peg to line up the workpiece for the second and subsequent cuts.
Hope that might be of interest.