What I use on mine though not as complex as yours are the tablets they use for cleaning false teeth. Break one up so slips down the neck then plug bowl hole, fill slowly to half full with hot but not boiling water. Leave it for a minute then slowly fill till the water starts to come out. Leave it for a couple of minutes to do it’s stuff then empty it to about half full and give a few shakes ,empty it then a couple of rinses with clean water and voilà done and shiny clean.
What I use on mine though not as complex as yours are the tablets they use for cleaning false teeth. Break one up so slips down the neck then plug bowl hole, fill slowly to half full with hot but not boiling water. Leave it for a minute then slowly fill till the water starts to come out. Leave it for a couple of minutes to do it’s stuff then empty it to about half full and give a few shakes ,empty it then a couple of rinses with clean water and voilà done and shiny clean.