We ran into this issue at AKV this past week. Talked to the front desk folks who claimed it wasn't a policy to disallow guests to use their own devices and sent up a runner to show us how to do this.
NB that the new TV setups do have an option to allow you to chromecast from an existing device to the new TV system. We didn't try it since the runner gave us the workaround.
The new TV system seems to be controlled by the phonejack cable that is also plugged into the back of the TV. The signal over this phone jack seems to provide a different "operating system" to the TV that overrides the normal menus that a Samsung TV has. Presumably that is also the data source that provides the new interactive features on the main screen ("welcome <Family Name>!") and the ability to view the guest folio and check out etc.
So if you unplug the phone jack from the back and remove the HDMI cable, and restart the TV with your own device plugged in, you can use the small button on the bottom back corner to control the volume and switch inputs, just like you could do before the upgrades. You *will* need to adjust the volume down, since it seems to be hardcoded to level 100/max volume when you turn it on. Since they removed the Samsung remotes in favor of the new system remotes, you will have to continually manually adjust the volume with the button on the back of the TV.
This is what the runner showed me, I didn't break any equipment etc. trying to figure this out.
If you're going to do this, please plug the room HDMI and phone jack back into the TVs when you leave so as not to make things difficult for the staff turning over the room to the next guest or to waste time for an AV runner to have to come up and fix etc. If you know what you're doing where these instructions make sense, please be a good guest and reset everything back to how you found it.