Interestingly enough, there's been a change in the 'official' aikikai finish to kokyu dosa/suwari kokyu ho recently, judging by the three shihan who've come to Israel from Hombu in the last 2 years. All of them were finishing facing uke's flank, with one hand threatening face/controlling nearside hand, and the other controlling farside hand, hip and supressing a possible kick. It isn't a pin, but a control of uke's escape exits.
I don't know if there was a formal change, or someone at hombu started doing it this way and it caught on. Anyway, I think its an improvement.
Anyway, Kathryn, this position isn't really a finish - the technique is only halfway done. We stop here so we can practice the initial movement as a breathing/relaxation/centering exercise. The real technique happens as uke tries to get up again.