Secondly, after the room is up to temperature, I tend to knock the
power rating down to reduce cycling.

Err, I think that last point is one that supports a 3kW fan heater!
You can only get up to temperature quickly and then turn the heat
down with a 3kW heater (or it's better at it).

I think you have misunderstood. In a room with a 1kW steady state
requirement, a 2kW heater will bring it up to temperature and then, on half
power, will be able to maintain it using only a minimum of annoying cycling.

A 3kW heater will bring it up even more rapidly. But then, turned down to
1.5kW, it is over sized and will switch on and off over a 3:2 duty cycle
with a period of a couple of minutes.

Christian.