I don't think there's anything in the Ecobee system that does that automatically like that.
It's not the most elegant, but it's not awful/ugly either, but what you could potentially do...
Wifi light switches, set them on a schedule perhaps?
https://www.amazon.ca/Kasa-Smart-HS2...43&sr=8-5&th=1
The previously mentioned Aqara looks like it could work too and be more automatic, but I have no experience with it to know if it'll work for your situation or not.
Ecobee sensors. Make sure they are compatible with your Ecobee lite.
https://www.amazon.ca/ecobee-EB-RSHM...4&sr=8-1-fkmr0
Then you can have it automatically kick in for certain rooms that may be a different temp than by the thermostat.
And lastly, if your furnace is high efficiency, just have the furnace fans on basically as much as possible to mix the air the home so that it's not as hot and cold in different areas.