When I did my "study", I considered the cuts, i.e. the stars should be spread around the sky so that stars with ideal cuts of star-90º-star for a two-body fix, or star-120º-star-120º-star for a three-body fix, could be found. I also considered magnitude, 1st magnitude stars being preferred over 2nd or 3rd. I selected an example and gave it some thought, and felt I made some progress.
For the example, I picked a random date, time, and location: 23 November 2005, 23:00:00 UT, L 50ºN, Lo 0º, for an LHA of Aries of about 48º. Pub. 249 selected Dubhe, POLLUX, BETELGEUSE, RIGEL, Hamal, Alpheratz, and DENEB, the ones in all capital letters being 1st magnitude, and Dubhe, RIGEL, and Alpheratz flagged as being suitable for a three-body fix. I found that there were 21 of the 41 stars visible (two right on the horizon), including the seven selected stars. If I eliminated those below 20º and those above 70º altitude, I was still left with 12 stars, the seven selected stars still among them. Dubhe, RIGEL, and Alpheratz were indeed well positioned for a three-body fix.
Capella and Pollux were at about the same azimuth and are both 1st magnitude, but Capella was still pretty high at about 69º, one degree under the arbitrary limit I set, so I eliminated it. Deneb and Schedar were at about the same azimuth, but Schedar was 2nd magnitude and still pretty high at 67º, so it was also eliminated. Rigel and Aldebaran were at about the same azimuth. Both had good altitudes and were 1st magnitude stars, but Rigel was significantly brighter, so Aldebaran was eliminated. Down to nine!
I then looked at the two that were not selected. I considered eliminating Menkar, being a 3rd magnitude star, but it was pretty much by itself azimuth-wise, so it stayed. Kochab was at a good altitude and about 28º from the next closest selected star in azimuth, Dubhe, so it seemed it should stay, considering that Betelgeuse and Rigel, two of the seven selected stars, were only 19º apart.
So now I was stumped. And even if I was able to rationalize eliminating Menkar and Kochab, I could not really get a handle on creating words to quantify making the selections. Eliminate stars with altitude below Xº or above Yº? If two stars had about the same azimuth, eliminate the dimmer one? If the two stars with the same azimuths had the same magnitude, eliminate the one with the altitude closer to the previously set limits? The list could go on.
I'm beginning to think Dave might be right about the experienced air navigators. When these tables were originally created, perhaps the selections were made by human "computors", doing it in much the same way I did. Must have been painful!