You typed in a long posting (10:09), but as you got the first sentence wrong, most of what follows is based on a fallacy.
There isn't a public sector pension SCHEME, there are pension SCHEMES. Only one letter different, but it invalidates all of your maths. Some of the schemes are perfectly viable and some are not. Why try to stupidly address themn all in one go. That is like trying to negotiate a cost of living increase (stop laughing at the back!) for every worker in the country at the same time - it can't be done. Each scheme must be addressed on its individual merits.
Some of the schemes had their contribution rates increased three years ago to allow for the increased average lifespan of the members, and are now completely viable for many years to come. Some of these schemes do not receive any government money, and any increased contributions will be syphoned off by government to help to address the massive budget deficits.
Got it now Alpha?