Please don't have a heart attack, but it sure looks to be true. Phone Arena's specs page is showing GSM world capabilities as well as Sprint's announcement, so I'm going to say that it's true if it's coming directly from Sprint.
As a person who owned a VZW LTE device, they still use the ESN to activate the device, and to block it from using the service if the ESN is registered in their block list.
4500ft is less than 1 mile, and the other 2 are within 2 miles from your house. You should have excellent coverage. Unless of course your house framing is made of metal. Then that could really cause problems. One question: Can you see the closest tower from your house?