How much can option market makers influence stock prices?

Your question lacks an understanding of how option market makers make a market. They are not a counterparty just sitting on the other side of you trade with the result that one of you wins and the other loses and in your example, to the tune of $4 million.

In addition, you are proposing that market makers are manipulating the market to screw you when you have a winning trade (eg. dump the stock to make sure that you don't win, etc.). It doesn't work that way.

Market makers hedge their risk. Read about delta neutral hedging.

Market makers have several ways to lay off the risk (conversions, reversals, box spreads, and other arb techniques). Here's an explanation of a conversion:

Suppose that you want to buy a $23 strike call. At the same time, I happen to want to sell the same series $23 strike put. Ignoring dividends (if any) and carry cost, the market maker takes the opposite side of each trade. He buys the put from me and sells the call to you while at the same time buying 100 shares, all done for a small credit.

The market maker has no risk because if the stock drops, he can exercise his put and sell his stock at $23. If the stock rises, it is called away at $23 via his short call. In this example, he doesn't care if the stock goes up or it goes down. He cares about pin risk but that's not germane to your question.