Thanks for the humility Jim. In case others read this, here's what we learned. We were told our boat uses 3/16. The last time marina serviced the packing they used 3/16. Another PSC owner used 3/16. So I bought 3/16. I also bought 1/4 just in case because I knew it was likely we would be unable to have access to supplies at times.
I was able to get to a dock lastnight and remove the old 3/16 packing. It looked in perfect shape and came off without any fraying I could find. (Not much water came in and I just wrapped a towel around the shaft so it would drip instead of spraying.)
Since the inspection of the packing looked good I hesitated putting in the 1/4. It was a tight fit but I was able to get it in using the side of a wrench. After each strip I tightened the nut up to push it in. I got three strips installed and hand tightened slightly. Today there is no water dripping but I'll recheck after break in. The shaft is not hot nor was it scored.
I'm still unclear what caused the bronze dust. Perhaps there was a small piece of thread caught on the shaft and turning in the nut.
PSC 31 #84