I had the exact same issue as OP, but seeing as this is months later I don't know if this is very useful...
I have the Sprint One in Chicago with great LTE all over, but I could never update the Facebook app or access Google Now. I also had trouble updating both the PRL and Profile, it would spin forever, then fail. I found out that the fbook and Google Now issues had something to do with LTE, despite testing at 30Mbps+, because everything worked fine on 3G or WiFi (LTE worked fine for web browsing, video and audio streaming, and etc). Turning the phone to CDMA only would fix all my issues (and 3G was fast enough, just not as fast as LTE).
I had gotten used to using CDMA only mode as a work around, but I just realized the profile/PRL issue might be related to the other issues I was seeing, so I switched it back to CDMA only mode and was able to successfully update both profile and PRL. Now everything works just fine on LTE.