There is no workaround for the iPhone 5 at this time. Verizon is supporting VOLTE on a very limited selection of phones, and based on what I've been hearing from Verizon customers, it's flakey at best.
GSM carriers like AT&T and T-Mobile have supported simultaneous voice and data since the beginning.
Technically, the GSM portion of your phone is unlocked and you could switch carriers without buying a new phone, but you will not get LTE service at all from anyone other than Verizon in the US on that phone.
Of course, slower data might just trump no data while you're on the phone...