Yes, there's a typo in #9, that's R hand forward.
Yes, Koichi Tohei's 22 kata is basically the 31 with a different count, and (usually) a greater emphasis on flow. There are lots of different versions of the 22 around, with different counting and techniques. There aren't so many variations in the 31, I guess because a) it's built from Saito's 20 suburi which most ki styles don't practice and b) there are plenty of 'definitive' tapes of Saito-sensei doing it.
Some dojo's practice both the 22 and the 31 as separate kata, as the version of the 22 they know is now far removed, and as I said the emphasis is different.
The version Greg gives a link to is quite an early one of Saito's. The description by Jon Diesch is a later one, similar to the version Saito does in the 1987 Aikido Journal tape. The main differences are in #9 (the later version is much more horizontal) and the last two-three movements.
Also note that Jon was describing the awase version, which is different to the kata itself (gasp). In the awase you end up one step further forward from where you started, due to #27, which is a backward step in the kata (and needs to be a forward one in the awase version).
There's also the different timings: Like Greg's link shows (with a regular beat), as if with a partner (including the parrying motions and allowing time for partner's attack renewal), and as a string of suburi (so that, for example, #5 and #6 are done in rapid succession - renzuko shomenuchi).
BTW, Eric - I agree with Greg - learn the 20 suburi.
Maybe there's a niche for me as a jo kata historian?