The Sams Photofact service manual is available for the Sony Trinitron KV27FS120 model, implying that this TV set is a consumer set, not a model specifically designed for hotels. Thus, it should tune the standard over the air and cable channel frequency assignments.
I really can't understand why a hotel would use a nonstandard set of frequency assignments. I am aware that some cable TV systems did assign the lower VHF channels 2-6 differently at one time, but I am quite sure that was done away with, later on. The only reason to do something differently, as best I can tell, would be to secure premium channels, if offered. However, that is usually done with an external box, or a TV model designed for that purpose.
From what you tell me, the TV has video and audio jacks for connecting the ReplayTV. For normal viewing, the TV connects to the hotel's TV room jack without a converter box. I am assuming that you are able to switch the TV to video input and see the ReplayTV screens. You get a message "no video signal detected" when you try to tune in a channel, even though you have detached the hotel's TV coax from the TV and connected it to your ReplayTV.
That said, you might try adding a splitter to feed the hotel TV signal to your ReplayTV and the room TV simultaneously. Both the room TV and the ReplayTV should be able to tune in the same channel.