Good to know they are pins. On your Reddit foto they look recessed. How would one get them out under normal conditions? Does it not run into the center of the screw shaft? Confused, thanks for jumping in.
The reason they look recessed in my photo is that when I took the photo, I hadn't yet had time to source new pins for the vise.
I am not the biggest fan of the round head pins / rivets, as they can be a bit of a pain to remove, and are mostly a 1 time use pin because you generally damage them when you taken them out.
If you are more concerned with functionality over originality, I would personally get some long set screws, turn them down slightly smaller than the diameter of the existing pins and then drill & tap the holes in the front jaw so you can easily replace them by just using an allen key to remove them and put new ones in.
To remove the existing pins, the only way I found to remove them is a bit destructive to the rivet heads of the pins, especially if they are original.
Use a small metal chisel between the rivet head and the vise jaw body to begin to pry them out of the housing. Once they start to move out, you can use a pair of visegrips to grip on to the pin and then pull them out.