Hi Jack,
Rather than referencing/copying from the Events Calendar page, create a new instance on the Home page, and then use the sub-calendar settings (in Events Settings) to include the calendar from the Events Calendar page.
If you look at the url's of the two items in your What's New, they both refer to the same ModuleID (mid), but different TabIDs. I'm guessing that the search process isn't clever enough to recognise this as being the same module, and I don't believe there is anyway the Events module could identify this.
Cheers
Roger