I was a little incorrect to say this couldn’t be automated. I have thought about (but not done anything about) a python script like the parts checking script that would take parameters like 120 pins and create the fzp and svg files with the xml for the connectors all defined. You would then need to use the svg editor to move them to where you want them, but at least the tedious editing work would be done. The right way to do it is finish the parts editor but that is a much bigger task.
Usually you don’t need any special tags, multiple pins overlayed on top of each other just work. I just find them messy and prefer to have them spread out (especially on something like this board with rows of sensor plugs) so that all the pins for a single part are in the same place.
On Inkscape (as noted I don’t know Illustrator, perhaps someone here who uses it can comment), we use the resize page to content button to reduce the viewbox to the edges of the defined component. If you don’t do that sometimes the scale gets off or the connectors are not aligned properly to the grid (although I’m not sure why that is). I don’t know how to do the same in Illustrator but I expect someone here probably does. I can fix it up in Inkscape for you easily enough, but if as last time that doesn’t translate well to Illustrator it may not help much.
Peter