I called Verizon this morning. I also chatted with Verizon online a couple days ago. I got different stories.
The online-chat CSR said that the Note 3 would ship before 10/10 and arrive to me on 10/10 at the latest (2-day shipping). I repeated back this arrangement to the CSR for clarification, and the CSR confirmed that I was understanding correctly. This was satisfying.
The CSR that took my phone call this morning said something different (and not in a good way): that the Note 3 may not ship until 10/10. But the CSR told me that I could return the pre-ordered phone if I wanted, with Verizon paying the return shipping. This means that I could still go to a Verizon brick-and-mortar store and directly buy a Note 3. And the CSR said that the local store may be willing to waive the activation fee to match the online store offer. I don't have high hopes, but maybe I can still have a Note 3 in my hands on 10/10/2013 without paying for activation, return shipping, or any additional fees. Or maybe my order will ship out this afternoon and arrive 10/10/2013. That would be much less of a head ache.