4x4mm QFN-16 to 3x3mm QFN-16?
[This is more of an extended comment than an answer.
I'm posting this as an answer, because I'd like to add a picture.]

You are not the first person to do that sort of goof.  At least, your footprint is larger than the actual part.  If it were the other way around, it would have been more painful.

Yes, correct-a-chip adapters are made and used once in a while.  There are even companies that specialize in such adapter boards (Adapters Plus is one I have talked to).

If I were in this situation, and this were a one-or-two-off prototype, I would wire the IC in a dead bug configuration.  As you've already mentioned, it's an RTC, so no high speed or thermal issues.

 (source: Screaming Circuits blog)