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No, there is nothing reserved. Users of the hotspot simply use whatever is remaining, you always get priority.
Have you tried all 13 wireless channels that are available on the home hub, just in case the three "smart" channels are all congested?
You will have to turn smart wireless off, and select each channel manually.
Because your TV has a rubbish wifi adapter / antenna?
or if you have a plug in adapter, it is behind the screen which acts as a big shield against the wifi signal.