* If it is a card edge, the offset nature of the connectors would make a very strange configuration for the module plugging into it. Staggered PCBs seems a little odd.
Your own pictures/drawings say that strange or not, the connectors are both used in an offset configuration for the ethernet cartridge. The PCB's don't have to be staggered, just the connectors.
* At around 5:20 in this video the engineer takes a module out of the system, and although he never shows the interface end directly, you can see (briefly) there is a connector vs a card edge:
The SCSI cartridge in the video appears to only use one of the connectors. I guess that's the nature of general-purpose expansion connectors.
* These laptops are really well made and having a card-edge connector for an external devices does not fix with the design of the system.
Let's flip that question. What would appropriate connectors for this design look like for an end-user quick-release future-expansion cartridge interface? We already know the answer isn't any kind of header pin arrangement.
* The Ethernet module manual shows what looks like connectors. Unfortunately it is all line drawings and there is no actual photo of the module.
* Some advertising for the 1500 Series shows a drawing of a module that looks like there are connectors.
You have a point. Perhaps some sort of right-angle panel-mount fingerboard connector was available back then? Unless you obtain good pictures of one of those unobtainium modules, you may never know. It's possible many of them only existed as prototypes and never made it to market.
Nonetheless, it doesn't change what it looks like. Odds are you can use a PCB for your interface to those connectors. You should be able to confirm that easily enough with simple experiments. Alternately, you could replace "Denny's" board entirely and interface to the easily-mated pin headers and do whatever you want if you need the quick-release feature.