I happened to come across an answer to this issue from a training video, so I'll answer my own question here.  There isn't a way to make ProConnect associate the carryover basis with a new Schedule E rental.  But what they want you to do is to keep the new and old properties as the same Schedule E rental.

So maybe to fit both addresses (or at abbreviations) into the Schedule E address field of one "property" entry.  And put the income/expenses for both properties on the same Schedule E property.  And that way when ProConnect puts all the depreciation on that same rental for both the new and old exchanged property, it's ok.  A side advantage of this is that it also retains any suspended losses associated with it since you're just continuing the same rental entry. 

It's a little weird and confusing, but it works.