Alternatively, rank the people on the "keep me posted" list by their network centrality within their group of contacts, invite the ones of more centrality first

Alternatively, rank the people on the "keep me posted" list by their network centrality within their group of contacts, invite the ones of more centrality first, and give them a limited number of invites to give away themselves. (That is: select evangelists from the "keep me posted" list, invite them first, and let 'em do their work.)