Well, I did read through the thread (again) and thought (again) about how the term is used by the Japanese I regularly encounter.
There is a lady who works at the check-out in the university Co-op here in Hiroshima and she uses onegai-shimasu several times during the payment transaction. Even after you have paid, picked up the bag with what you have bought, and made to leave the check-out, there is still a final 'onegai-shimasu', to send you on your way. I do not think the phrase has any specifiable meaning here. It is similar to suminasen, used in almost the same way by the lady who runs my local sake shop. Here there are three or four sumimasens uttered each time I make a transaction, usually interspersed with one or two doomo's (but never doomo-doomo).
The weather is very hot and humid here, with daily temperatures in the mid-thirties. However, encounters with neighbors invariably start with stating the obvious: atsui desu-neee (with the length and pitch of the neeee adjusted according to the temperature) and I have sometimes wondered what answer they are expecting, if any. Inevitably, I vigorously agree and go on my way.
So in the local dojo, there are many more of these 'phatic' occasions, where you utter phrases like onegai-shimasu, simply as a means of social lubrication: somewhat like drinking green tea.