You should call multiple family law attorneys in the Gillette area and ask for a flexible payment arrangement. You are right to assume that some attorneys will require you to pay a large portion upfront, but others may work with you in setting up a flexible payment arrangement. I am not a family law attorney, but I know that some do offer flexible payment plans. If you don't know where to start your search, use this link to the Wyoming State Bar website. This will help get you started.
https://www.wyomingbar.org/for-the-public/hire-a-lawyer/