This is awesome and I love it! Congratulations, and welcome to realizing that once you can make things, you can make exactly what you want, regardless of whether it's practical or economical (as you discovered). If you have a partner, good on them for not joining the pool for 2034 or stabbing you with the aluminum partway through the project.

A couple notes:

The customary solution for hanging something on a wall such that you can hang and un-hang it is a French cleat [0]. They're best for flat-ish stuff, but they work pretty well for shallow cabinets as well. You have a cavity in the framework that you can hide it in, along with the electronics.

I don't have a huge beef with using aluminium for the frame, though I'd have used aluminum personally. I agree with others that wood would have been cheaper, but I'd be generally worried about the electronics in the cavity not getting enough airflow to stay cool. The brick wall should sink some heat, and the aluminum should help move heat better than wood would. Honestly, I see the aluminum as a pretty expedient solution to prototyping this. You don't need to save every penny if you're only making one of something.

Wood movement is a thing. I'd edge glue the two pieces of beech, and then follow the traditional solution of mounting to the frame with one fixed point and one floating point. Using a wood frame wouldn't have gotten you out of this: in practical terms, wood is constant in length, but has noticeable changes in width. Attaching pieces with the width running across the length is called cross-grain construction, and is best avoided. A common solution is table buttons[1].

For affixing router templates, double-sided tape works well. You want the stuff with the thickness and texture of duct/duck tape, sometimes sold as carpet tape. Don't use the thin stuff from the office supply. DON'T REUSE THE TAPE. It never sticks as well the second time, and a router can do a lot of damage in a hurry if the template moves. You can also just use a single sheet of paper glued between the template and the workpiece. This is called a paper joint[2], and it's commonly used for split spindle turnings and bowl turning.

Anyhow, the design is great, and it brings a lot more to the space than either of the commercial options. Keep on building, and please keep posting!

Thanks also for listing parts/suppliers/etc.

[0] https://en.wikipedia.org/wiki/French_cleat

[1] https://www.popularwoodworking.com/editors-blog/attaching-a-...

[2] https://www.wwgoa.com/video/bowl-turning-paper-joints-000224...