A treasure indeed!
Regarding the 31 kata - It seems like O-sensei didn't do many things exacly the same twice. Specially when it came to doing long jo kata. It seems, however, like there was one that he did farely often and farely similar. This is what is today known as the 31 kata. Saito sensei saw it so many times that the overall kata became apparent to him. O-sensei, however, probably changed some sequences at will including and excluding some parts. He might have started with choku tsuki instead of kaeshi tsuki (like in this version!). Hi might have added a hasso movement in the end etc. Over all it looked like the one we see today.
Then O-sensei seemed to have done another long and more free sequence of fluid movements including alot of the nagare gaeshi, hasso (btw I meant that today there are two of the five hasso suburi - hasso gaeshi ushiro uchi and barai - left in 31 and 13 kata), ushiro tsuki, sometime from one knee on the mat, the large katate sweeps etc and in all directions. Simply just combining the single sequences in all possible way in some form of imaginary purifying fight. Therefore it never looked exactly the same from time to time.
Sometimes I play with this myself, just playing freely with the jo in an endless flow of sequences possible. A good way of breaking the box around your mind.
I believe that's similar to what Saito sensei did in the second form. Just a lengthy flow of alot of the single sequences he remembered O-sensei used to do.
It's interesting to view Tohei sensei do something similar as well.
Tohei sensei formulated, in a similar way like Saito sensei did, a kata not very unlike the 31 kata, but with a slightly different count and with some other sequences in and some not. This was called 22 kata. (Can be viewed here
performed very nicely by Peter Spangfort, Järfälla aikido. Just click the link "jo kata 22 at the top.)
But Tohei sensei also often seemed to have done these longer and more free sequences as can be seen here
in aikidojournals video archive where Tohei sensei was demonstrating aikido in Florida 1967.