If a sufficient number of miners began using the new protocol

So say that these miners, who are incidentally nearly always owners of significant numbers of bitcoins decide that they want to inflate the currency and voluntarily devalue their assets (because people totally do that kind of thing).

• They announce their intention to do so far in advance.
• They fork changes to both their mining software and at least one bitcoin client. (They can't change the reference implementations. They have no chance in hell of persuading Gavin Anderson to change the official bitcoin software in violation of the prohibited changes list.)
• They try to convince all uses to download their modified clients. They have to overcome all (rather rational) fears that this new currency is unstable in as much as even the fundamental aspects are changed at whim. They have to overcome the (entirely rational) fear of each individual that if they accept NotBitcoins then others may not, whereas if they accept bitcoins then NotBitcoin users must accept them. The users have to not care (or be kept ignorant) of the fact that their client is incapable of distinguishing between two inherently different currencies.
• They have to somehow prevent any of the other people in the world with a vested interest in maintaining the value of bitcoins from doing mining. Even if the current miners ignore their own rational incentive to maintain the value of the coins they just mined, everyone else has years in which to set up hardware to do mining. And wouldn't need years. They need days, even assuming not a single existing miner defected against the inflation alliance.
• The "51% of computing power" metric which is relevant to different histories of the bitchain is irrelevant. If the inflation alliance manages to have 20 times the computing power of those who have created miners for the original currency all that serves to do is create massive incentives for inflation alliance members to defect back to the original currency. Their hardware and electricity costs become suddenly far more productive at creating bitcoins in the conventional bitchain.

In other words; if enough people think a permanent finite supply of bitcoins is a bug, it will be treated like previous bugs in the block chain.

Send in the clergy! They can move diagonally!

You are treating the bitcoin economy as if it has the same rules, incentives and capabilities as a country with a government enforced currency and a central bank which implements monetary policy in pursuit of political objectives. However, these similarities are superficial. The actual microeconomic incentives, available tools, problems, goals and powers are not the same. Your proposal requires many actors to do things that go against their personal self interest voluntarily. That isn't how the world works.