If after a factory reset Bluetooth is not working, I would call Asurion and get another replacement that does work... plain and simple. If it doesn't work on stock, the chances it will work on anything else are near 0, and unlocking may void your warranty, resulting in a charge to you if they have to replace it later.
Current Personal Phone: Google Nexus 4 on AT&T (KitKat 4.4.2 KOT49H/GoPhone)
Current Work Phone: LG G2 on VZW (Beanstalk 4.4.2
Current Tablet: iPad 4 and Nextbook 8 Premium with marxo's N8+ ROM - Revision 1b2 (ICS 4.0.4)
Previous/Retired Android Devices: HTC Aria, HTC Incredible 2, Samsung Stratosphere, HTC Rezound, Samsung Galaxy S2 Skyrocket