My present Plan A is to remove the platform, swill it about in alcohol, re-lubricate, and stand by for perfect operation.
NO NO NO.
The platform needs to be completely taken apart polished and rinsed, then cleaned in a proper cleaning machine. The only part that is not to go in the cleaning machine is the hairspring. A good clock repairer should be able to do this for you. If you damage or break any part it could cost a small fortune to put right.