@evanevery I totally understand your reluctance to manually add 64 rivets to your board. I do want to say that after you get the hang of riveting, it is actually quite a fast and low-effort process. 64 of the large size would take you maybe 10-15 minutes from start to finish, with the bulk of that time being spent inserting the rivets into their holes prior to riveting and then doing continuity tests (& possible re-riveting or soldering to fix opens) afterwards.
Beyond simpler PCB routing, the real advantage you get by taking the time to add rivets is dramatically increased mechanical strength and reliability. I’m not sure what the use case is for your headers, but if you plan on inserting & removing anything more than one single-pin connector at a time (i.e., jumper wires), you are going to be putting a nontrivial vertical load onto your header. Without rivets, the only mechanical connection your header has to your board is through the solder joint between the pin and a PCB trace (if one is routed to that particular pin). That is an incredibly weak connection and it doesn’t take much force to break the trace, which is fairly brittle when baked. You are welcome to experiment with rivetless headers for your application, but unless you are quite careful and use low-pin-count cable assemblies that allow you to minimize insertion & extraction force, I suspect you’ll start seeing continuity failures after using your board for a little while.
You could also try a compromise: Add rivets to holes strategically. E.g., one or two on each corner and one every other pin, or only on those pins that have traces. So you don’t have to do all 64 but you’re still getting some increase in mechanical reliability.
Edit: I just re-read your original post and saw that your use case is to attach this board to another board. I would strongly urge you to use rivets on every pin in that case. That is a huge insertion/extraction load if all 64 pins are involved simultaneously.
