Don't think it's possible. I read US Cellular's unlock policy and they mention 1x and 3G devices only. That disqualifies your 5c.
Which leaves a third party unlock service or a SIM interposer (R-Sim, Gevey, etc). No idea if a third party can do it, especially if US Cellular is like Sprint in that regard. If so, then this is not possible except with a SIM interposer.