I couldn't reach it with my fingers but improvised and created this tool. Some sandpaper glued to the tip of a thin screwdriver. This allowed me to get to the problematic spot and remove enough glue that the wedge now fits. Problem solved.
Other than that, frame looks ok. The bottom bracket screws in easily, without any issues. The headset and fork assembles well, with no significant gaps.
I'm starting to assemble it, but to finish it I still need the wheels, which I only ordered 3 days ago.