Followup - to help future others doing what I'm doing ....
In a multi-store setup GenerateOrderCustomNumber will use the default store settings with regard to what custom order mask to use. I needed it to use a specified store's mask. So what I did is:
var cnf = new CustomNumberFormatter(_settingService.LoadSetting<OrderSettings>(iStoreId));
ordNop.CustomOrderNumber = cnf.GenerateOrderCustomNumber(ordNop);
I can confirm this works. So unless you see a bunch of replies below this message saying "NO! NO! NO! NO!", you can assume that this is the right way to do it. <wink>