Best Carrier for iPhone in the USA?

So I have been with AT&T for over a decade and got my first iPhone in the summer of 2009 (the iPhone 3GS) to replace my Palm Tree 680. There was a time when AT&T customer services was awful, but recently it has been quite good (since they lost iPhone exclusivity). With my corporate discount I am paying $118 per month for 2 iPhones with 750 shared minutes with free night-and-weekends + rollover (I have thousands of rollover minutes accumulated since we never hit 750 minutes). We also pay $5 per phone for 200 text messages each and with iMessage this seems to cover us. Then each phone gets unlimited data which is throttled at 3GB. So far I have not been able to find better pricing even with the shared data plans, but the need for unlimited texts and more phones is approaching as my three kids get older. Additionally, my wife's involvement in PTA may require more text messages since only half of the PTA board members have iPhones and can iMessage.

That said, my first iPad was on AT&T, but after a trip to Idaho Falls and its surrounding areas where AT&T had nearly no coverage at all I decided that my next iPad would be Verizon so I could have a better chance at connectivity when traveling. My Verizon iPad 2 was replaced with a Verizon iPad 3 with LTE (and tethering that only Verizon allows from iPad). I have come to like Verizon because of the data speeds. Oddly, because the community I live in fought the construction of a new cell tower a few years back (it is being proposed again) the AT&T LTE coverage is better near my home and community than Verizon's (I'm sure folks don't hear that much).

Now the next iPhone is suppose to have LTE support. I can keep on with a Verizon iPad and AT&T iPhones or I can look to consolidate under one of these shared data plans. I figure a 6GB shared data plan is as good or better than 2 x unlimited with a 3GB throttling limit. My iPad uses less than 500mb per month normally and our iPhones usually do not use more than 700mb per month. However, I have concerns switching to a single carrier for everything:

1) AT&T coverage in rural areas (which I do travel to for vacation) is going to be awful

2) Verizon LTE iPhones will likely have simultaneous voice & data support, but they won't when on CDMA 3G (this is really annoying to me)

3) Verizon LTE has more coverage but supposedly AT&T LTE tests where they have coverage have been shown to be faster on some reports AND the fall-back from LTE is speed HSPA+ @ 21Mbps (theoretical) whereas CDMA is the fallback for Verizon.

4) Not sure about how Sprint factors into this -- their plans are per phone and look expensive.

Can anybody provide any help or suggestions? Or just share your own experiences.