Can I see who is one stamp away from a reward and give them a push?

Yes, through a campaign. Under Marketing → Campaigns the audience list includes Close to a loyalty reward, shown whenever your loyalty programme is on. Write a short message, pick that audience, and it goes out under your weekly cap in the daytime window. The card on their phone already shows how close they are, so the message is a reminder rather than news. The Promotions & marketing tab in the docs lists the campaign audiences.