The best thing I could suggest is submit daily. The reason why is because different engines index once every week and others that index every couple of months. It is better to submit as early as possible that way you will have your site looked at by both of the engines mentioned above. Do you want to have the new site listed as soon as possible? Or do you want to see how the changes will effect on your listings?
We have many sites and pages. I usually leave my pages alone once they are indexed. We have changing content and text navigation links at the bottom of the pages, this seems to help. Our listings stay pretty solidly in place. I give it 6-8 weeks after the first submission, re-submit as needed if not listed yet. I agree, submit small amounts of pages at a time.