Sprint has a standard "box test" according to Tier 3 support that can test 3G and GPS on any phone. SamuraiBigEd had that done.
Don't doubt that perhaps testing LTE is an issue today but your issues don't rise to that.
Make sure to do a PRL then Profile update.
I certainly hope that they didn't hand you someone else's problem phone or a phone from the same possibly problematic production run.