I understand that SPRINT is going to continue to refuse to unlock it, but I also understand that outside of programming, all iPhone 5s phones have the same CDMA/GSM transmitter capabilities both domestically & abroad.
So I find it hard to believe no one will come up with a way to completely unlock SPRINT/Virgin Mobile USA iPhones. There should be no physical reason inside the phone to make their version different or completely prevent it.
This is not the case at all with Sprint iPhones... The Sprint Model of the 5, 5S and 5C are different than all the others -- and tailored to their specific bands and to the bands in Japan.
The 5S as the example here, Sprint is Model A1453. AT&T/T-Mo is A1533, and the Verizon model is also A1533, but with CDMA enabled (otherwise not available if you buy one for AT&T or T-Mo). The differences really lie in LTE, 1453 has LTE Bands 1, 2, 3, 4, 5, 8, 13, 17, 18, 19, 20, 25, 26. 1533 has LTE 1, 2, 3, 4, 5, 8, 13, 17, 19, 20, 25.
Sprint models are totally SIM locked domestically from the baseband version they use. No unlocks are available. Starting February 11, 2015 -- Sprint has committed to allowing domestic unlocks, to adhere to the new unlocking law (which actually states this must be the case by January, but whatever). Whether this transcends this date, and hits this new iPhone is unknown at this point.
I am unsure if a jailbreak would help you on your way, but then you'd have to be willing to do that if it does.