This project has been stalled out for quite a while due to my lack of knowledge, funds, and working hardware. I recently found the 8086 makes an eMMC HAT that works with the Pi 4 that only requires a quick edit to the config.txt file. I failed to get the SD flash chips to work previously and gave up for a while. I just found this HAT and decided to start looking into this again. While not exactly what I'm looking for, it is close enough to allow me to actually get this working and start developing software for the system. The SD flash chips act just like an SD card, but in a smaller and cheaper form factor. I plan to order a few of these HATs quite soon and will start testing when they arrive. I still dream of making my own custom cartridges for the Pi 400, including boxes with proper box art, instruction manuals, and all sorts of fun features. I start learning KiCAD soon and will get some rest PCBs ordered.

Update: Found a link to said device.

eMMC HAT for Raspberry Pi