Regret can't help with the TV, but know the problem ! Service was terminated at the apartment we've just rented for exactly that.
Would never recommend SatPhone option as notoriously unreliable and expensive. Really only an option if no conventional cell coverage.
Luckily, when using Cellphone networks for this sort of application, signal doesn't have to be as good as when being used for voice calls. If Sim card 'data enabled' it will generally support data transmission in areas where you can't get decent 'voice' contact, although it may take some time to complete a transmission. (Similar principle in text messaging, you can generally get a text out when you can't make a voice call. )
This is the same sort of system I'm selling to Local Authorities here in the UK, for monitoring 'FlyTipping' in remote areas, ASBO's, etc. , but it does depend on reliable cell networks, and a service provider that can support mobile data.
I'm sort of surprised that no local company out there seems to offer this sort of equipment as it's well within the capability of any decent electrician to install it, with support / backup from local IT company & cellphone provider.
Would be happy to discuss possibilities with any local companies that may be interested.
Cheers,
Jim