Can the re-order nudge say something different each time, in my own words?

Yes. Under Settings → Automations, Re-order nudge, the box Your own wordings takes one message per line, with {restaurant} for your name, {link} for your ordering page on every line, and {code} for the coupon if you give one. Each nudge uses one of them and never the same one a customer got last time; leave the box empty and we rotate through our own wordings, listed on the page. The Orders & delivery tab in the docs covers the nudge.