Sounds complicated? I know you probably want to use what you’ve got but heatmiser fan coil stats are good
https://heatmisershop.co.uk/app-control-fan-coil-thermostat/
It has 1 call for heat and 1 call for cool, used a relay to switch a volt free connection on my heat pump. Has a 2c deadband, my set up is heat to 20c and cool from 22c, flick automatically from each with both having weather compensation. If you get the neohub you can automate IFTTT app with octopus energy rates and local weather forecast, this service is all free.