There are ways to speed this up. Depending on how you value your labor and where your production bottlenecks lie it may be worth it to investigate.
Stickers or a stamp for the maker mark on the bottom instead of being engraved is one way. Engraving is notoriously slow no matter which model of Glowforge you have, but those are small engraves so maybe that’s not the main driver of your duration. I’d be willing to bet it’s at least 5% though and time is money.
Thinner materials. Especially ones that are not MDF core. MDF is a difficult and dirty material to cut, switching to a wood core plywood and especially a thinner plywood will make a huge difference in your cut time.
The trade-off with using a thinner plywood might be a strength issue. I find that 1/16 plywood is much stronger than you might think, and the fact that you’re making boxes — which are self-reinforcing by nature — might make it feasible. Besides, looked at in a certain lens a little fragility is a feature not a bug. If someone breaks their favorite lantern maybe they’ll buy another one.
This stuff cuts so quickly it still makes me laugh when I use it. It’s satisfying.
Anyway nice execution of the interchangeable lamp concept. This is one of those types of projects that a lot of people get the idea to do but almost nobody follows through to the extent that you have here. You’ve really explored it, and I know that that process takes time, focus, and effort. Good job.