What do I do when I've filed an amended return and it's nearly 1 year later, no refund given? I've called the IRS and can't get through. What should I do?

You can contact your local IRS office. See this IRS website for local IRS offices - http://www.irs.gov/uac/Contact-Your-Local-IRS-Office-1 or call 1-844-545-5640 to set up an appointment
Or you may want to contact a Taxpayer Advocate in your area. See this IRS website for Taxpayer Advocate in your area and a toll free number - http://www.irs.gov/Advocate/Local-Taxpayer-Advocate

@joshgates7 it is taking 9-12 months for an amendment to process.  Have you checked the Where is my amended return on the IRS website? The customer service reps aren't going to know any more than what is on the website, so suggest having patience and not calling them. Note the FAQ below states 'more than 20 weeks', so there is no upper bound to how long it will take, but others that have posted (as well as my own experience) appears that it is taking 9-12 months. 

Status of Processing Form 1040-X, Amended Individual Tax Return: As of July 30, 2022, we had 2 million unprocessed Forms 1040-X. We are processing these returns in the order received and are working hard to get through the inventory. The current timeframe can be more than 20 weeks instead of up to 16. Please don't file a second tax return or contact the IRS about the status of your amended return. Taxpayers should continue to check Where's My Amended Return? for the most up to date processing status available.