So I finished beveling the box parts and didn't have any safety issues. Since I had a sacrificial board on the miter slide I'm not sure how I could have used any finger boards. I did the pieces over 3 or 4 days, probably about 4 hours total router work.
Yes, I could have done one or two edges (depending on whether it was a side or bottom piece while the stock was still longer but I have a couple of questions/comments about that. My stock was about 8 to 10 feet long and that seems to me to be too long for a "normal" router table. I could have cut the pieces shorter, but when I was cutting to length I had to cut out knots and such and didn't want to waste wood.
Yes, that could have been penny wise and pound foolish.
Maybe the scary part of this is that it worked and there weren't any scary moments. I did run the pieces in batches of 15 to 20 and I would stop in between batches to stack the beveled pieces in the box, take the next set and sort out which sides would show and stack them all in the same direction, grab a drink of water, put the mask back on, etc - so it wasn't a single session of just slamming pieces through the router.
I had a couple of minor incidents when I was cutting to size on the table saw (which was done in a more sustained manner) and decided that when my fingers were closer I needed to change the way I worked.
I appreciate all your advice and concern. Just for the record, I realize that whether it's a blade with teeth or one with a cutter head they spin very fast and flesh is very fragile. It just seemed safer and more accurate to do this on the router once the pieces were cut to size.
I will look in to how to do it differently as this certainly won't be the last time I'm building boxes like this.