The frustrating truth is that once the warranty expires, you're generally out of luck with the manufacturer - that's pretty much how warranties work. That said, you do have a few options worth exploring. First, check if you used a credit card to buy it. A lot of credit cards offer extended warranty protection or purchase protection that kicks in after the manufacturer's warranty ends, so it's worth calling your card company to ask. You might also have consumer protection laws in your state that require products to be "merchantable" for a reasonable period of time - some states give you a few years to challenge a product that fails prematurely, even after the manufacturer's warranty is done. It's worth looking into your state's consumer protection laws or calling your state's attorney general's office to see if they have any guidance.
Beyond that, you could try reaching out to Maytag directly with a polite but firm complaint about the timing. Sometimes if you explain the situation clearly - that it failed almost immediately after the warranty ended - they might offer a discount on repairs or a partial refund as a goodwill gesture, especially for a major appliance like this. It doesn't always work, but it costs nothing to try. You could also look into whether an independent repair shop might charge less than the $400 quote, or whether the repair is actually necessary or if replacing it makes more financial sense at this point. Sometimes a $400 repair on an $800 machine that's already failed once makes you think twice about sinking that money into it.