When dealing with recalcitrant agencies, governments, businesses or otherwise who move very slowly or refuse to deal with genuine consumer issues - like refunds they have agreed to - one thing to do is carefully up the ante. You need to get them to take you seriously, and one way is to potentially get some third party help.
Call the hospital billing department and say if they don't resolve this issue - which they admit exists - you're going to file a complaint with a consumer advocate, like Nevada Consumer Affairs .gov and/or get legal help from a non-profit or pro-bono legal aid firm, like Pro Bono Legal Services - State Bar of Nevada.
I say carefully because you don't want to say I'm going to sue! or get angry and threaten anything. Just tell them you're looking at all your options. And that may resolve the matter right there; they don't want to deal with the extra work of a complaint from the state government or a letter from an attorney, and you may have your refund quickly.
If it doesn't, look at filing a complaint with the online form at Nevada Consumer Affairs, or call a free or pro bono legal clinic and see about getting help. Sometimes a formal complaint or a letter from a lawyer will quickly resolve things.