You've answered your own question. Putting the thermostat near a heat source, or having heat sources in some rooms, not others will always unbalance the system leading to hot & cold rooms.
If you want a warm climb into bed, get an electric blanket (or a lazy dog. :-) ) Moving the thermostat to a different location will likely make the living/family rooms extra-warm when fully occupied.
The alternative is to micro-zone the system, which can lead to short cycling and lower efficiency with old massive boilers unless you swap out the fin-tube baseboard for something with much higher water volume, or use a buffer tank as a hydraulic separator, plumbing it primary/secondary. (It becomes a real hydronic design problem.)