http://sensorly.com/map/4G/US/USA/Sprint/lte_310sprint#q=60018
http://sensorly.com/map/4G/US/USA/Sprint/lte_310sprint#q=60016
http://sensorly.com/map/4G/US/USA/Sprint/lte_310sprint#q=60068
This covers pretty much Park Ridge, Mount Prospect, Des Plaines, & Rosemont
I will be able to contribute more next week when my LTE Device actually arrives, but according to Sensorly we have pretty good coverage in our areas. Have you tried the suggested solution of setting the phone into airplane mode?