This is over-complicating it! Surely the OP can just close the valves at each end of the rad and continue allowing the contents of the rad to trickle out until it stops?
As others have said, care will be needed to prevent the dregs of black water pouring out onto the carpet. A couple of old towels will do, or a helping hand from someone else to tip the rad so it all pours out one end.
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