When should we make calls to make a minyan?

General policy as per the ritual committee is to make calls to fill a minyan when there is someone present saying Kaddish or with a Yortsayt. This can't be done at Shabbat mincha as we don't make calls on Shabbat. But what about when there is a Torah reading? I would think that we wouldn't want to fail to have a minyan any time there is a Torah reading. And what about our Russian gentlemen? They find it very disturbing when we don't have a minyan even if there isn't anyone saying Kaddish or with a Yorstayt. They are elderly and their attendance is an effort that deserves to be dignified by the effort of a few phone calls. I follow the lead of the ritual committee here, but with qualms.
Who and how soon should we call? In the evening I will make calls starting at 6:00 PM. When do people start making calls in the morning? People often arrive later than the starting time of morning minyan and sometimes at evening minyan. In the evening I don't count on late-comers. Not sure what is done in the morning, but I know that there is some annoyance about this issue in the morning. When I make calls in the evening people often demur, but nobody tells me don't call at this time. I imagine it is harder to figure out who it is OK to call at 7 AM. I call only people who are within five minutes of the synagogue and I think that to do otherwise is not appropriate. Kenny has suggested that we call people ahead of time if we think we will be short of people. I agree in principle but hate to be nudging people. For Shabbat mincha calls ahead of time would have to be way ahead of time. It would be good if we could get a head count Shabbes morning. I do that informally when I remember, but it would be good to have a more formal procedure.