It would be useful to know if this rad has always been cold since the house was built, or if it started out hot and gradually got worse.
As you have a header tank, and there is at least a bit of flow through that rad when you turn the others off, why not put in a sediment-loosening chemical such as Sentinel X400 and see if the water turns black (which will mean it is starting to loosen old sediment) and run it for 4 weeks before draining?
Or, if you don't want to take up part of the floor, have you considered running a new pipe just above skirting level?
I am not a pro
As you have a header tank, and there is at least a bit of flow through that rad when you turn the others off, why not put in a sediment-loosening chemical such as Sentinel X400 and see if the water turns black (which will mean it is starting to loosen old sediment) and run it for 4 weeks before draining?
Or, if you don't want to take up part of the floor, have you considered running a new pipe just above skirting level?
I am not a pro