I had no problem giving Apple a $930 hold on my credit card so I could determine if a HW swap would work, if that is an issue for you, I definitely understand. Keep in mind that Apple has sold how many million of units to VZW customers. There are only 100 or 200 of us complaining and I have a bunch of friends who have VZW LTE phones and are experiencing no problems, which is why even though I was convinced originally it was a SW problem as well, I am not as convinced.
Perhaps I will be convinced back to my original theory of a SW problem if the replacement HW shows up today and doesn't work.
Either way, if you guys are just sitting here posting complaints in this thread and not calling Apple's 800#, they are not working on this problem for you. So even if you don't want a HW swap, open up a case and report your symptoms. I will report back to this group immediately after setting up the device to either report that the HW-swap has the same problem or that it fixed my issue and then you guys can decide how to proceed.
The only thing I ask is that you call the 800-MY-APPLE and open yourself up a case. There is no cost to do this and they cannot be aware of how serious a problem they have (whether it's SW or HW), unless they are being told of this. Also, while you're at it, open up a VZW case as well. When I opened mine up, supposedly nobody else in the country was reporting it to them either 🙂
BTW - field test menu is under Phone *3001#12345#* Call, this will report -112 to -115dBM for me most of the time I have a LTE signal.