Possible to get my router moved and rewired into a different room

Does the other room have a coaxial cable wall outlet / line ?

Ok so Comcast techs do not do wall fishing for the coax wiring. They will only install wall plates / outlets on a wall that faces the outside by running external wiring on the outside of a building and drilling a hole through from the outside to the inside to get the wiring in. If you want / need wall fishing, you will need to hire a local contractor such as a low-voltage electrician. They also refer to a service company that they have partnered with. See this article: https://www.xfinity.com/support/articles/hellotech-overview