Happy to look into this for you. What is the name of the theme that you are using?
I was able to find this older forums post here that has provided some code on how you can show prices on your sold-out products. With that said, it's not officially supported by Shopify and I do recommend duplicating your theme first in case any coding issues arise, you still have a working version of your theme.
Shopify has an experts platform that allows you to find and hire a developer for small and large coding gigs. With the help of an expert, they could definitely help you do this at a modest cost. If you would like to learn more, feel free to check out our Shopify experts directory.
If there is anything else I can help you with, please let me know.