I got the breakout boards that I've ordered from OSHPark in the mail today. Unfortunately, as you can see on the picture, the OSHPark panelizing process put "mouse-bites" on all sides of the PCB edge connector.
This is really annoying, because this means I need to get those off entirely before I can use the boards. So far, I quickly did this for one of the boards and it does seem to fit. However, I do think I will need to reduce the width of the connector just a little bit in a next iteration. Besides that I'm still unsure about the thickness of the PCBs. These are 1.6mm and, while they do fit in the connector, I need to apply just a bit more force than I would like to. This makes me think that the connector might suffer from it and perhaps it will not work that well anymore with the official connector on the Gameboy consoles.
Hopefully, in a next update, I will have sanded some of the boards, soldered headers to them and hooked them up to a logic analyzer. ;)