Verizon is just being idiotic. US Cellular uses the same network technology as Verizon (well, technically the same as Sprint, but fully compatible with Verizon), so you should be able to use your phone with them just fine (US Cellular is a CDMA/EV-DO/LTE network provider). US Cellular iPhones are not carrier locked to begin with (at least not so since the 4s as they stopped locking things back in 2014 or so).
All you should need is a Verizon SIM and an account with them. Stick the Verizon SIM in and activate service - Verizon proudly claims you may bring your own iPhone 7 for use on their network, so why they would tell you that phone cannot be used is beyond me.
Try just not telling them where you got your own iPhone 7+ from and tell them you want to set up service and will be bringing your own "compatible" iPhone with you.