Imo having a pronounced "lip" on the front baffle can be detrimental. Are you up for an experiment?
We're going to simulate a lip around a baffle. It won't be a perfect simulation, but then simulations never are.
Extend two fingers on each hand and place them up against your face, on either side of your mouth, as if they were two of the four sides of a recessed bass cab face. Now talk. Note the timbre of your voice.
Remove your hands and talk again. Hear the difference? Go back and forth a few times. Now this difference is probably exaggerated compared to the situation with a bass cab, but I grew up doing high-end home audio and we tried very hard to avoid that "boxy" signature.
Now to see what happens with a cab like your Hathor 1855, with the criss-crossed mids, use your whole hand, but only on one side of your mouth. Compare that with no hands, and there's a little change but not much. But use both hands and ugh! That's why we have that triangular cut-out in the top just above the mids.
Does the thick wooden section in front of that triangular cut-out cause a problem? Well, let's simulate that. One hand open on one side of your mouth, and then two fingers on the other side, but instead of up against your face, about 1" out in front of your face. Talk. Then remove the two fingers, and talk again. Negligible change.
So anyway in my mind at least, there's some madness behind the method, or vice versa.