Whatever you do, you definitely need that pin. According to the diagram I'm looking at, pin A1 is BR, which I'm pretty sure is Bus Request. Without that, it won't be able to participate in bus arbitration.
Is the pin header through-hole? That is, does it have pins that extend through the PCB? Or is it surface mount. If it is through hole, I bet you could remove the old pin and desolder it. It would be nerve wracking though to make sure you don't damage nearby pins and don't damage the through-hole copper in the circuit board. And you probably would have to do something like cut the plastic matrix around that one pin. Although, if the pins are wider closer the board, as you suggested, you may be able to carefully pry the entire plastic matrix off of all the pins, replace the problem pin and then replace the plastic matrix.
Alternatively, identify any nearby connection points for that signal on the SE/30 logic board. Solder a small wire to one of those connection points (e.g. wire wrap), and then install the upgrade and attach the other end of the wire to the pin (A1) where it pokes through the top of upgrade circuit board. You might even be able to solder a longer pin on there, and put a terminal on the end of the wire, so it can just slide over the pin, making it removable.
But if you have the clearance, DN's suggestion is probably the easiest and most reliable.