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To decommission the aga, I assume the attic water tank is also no longer used, if so you need to first drain this tank. I would suggest you access the water tank in your loft, and then check if there is an overflow. If there is, I would use the overflow to empty the tank in the attic, this way you can observe the water reducing, and if the wrong stop cock has been closed you will hear the tank filling back up. If the tank is still in use by your new heating system, you can ignore this step.
In terms of the aga, you should have two pipes from and to the aga, which circulate the hot water. Bleed off one, as you suggested earlier, you will find by opening the other slightly it should allow air in and help siphon the system faster.
It may take hours for all the water to dissipate fully, so suggest once you cut the pipes and free the aga, you cap off the pipes tp stop any residual water making its way out and causing a damp patch, weeks later.
Moving the aga by brute force is the quickest way assuming you have the man power, if your doing this yourself, I would look to break it down, by taking the top segment off, removing the back boiler and then try and move it in three pieces.
Please let me know if you need any clarification, if possible please provide photos so I can visualise your specific setup.