Edit: Before editing anything, make a copy of the entire folder named after your farm, and place it on your desktop. If something goes wrong, you can replace the folder with the copy from your desktop.
I let the furniture sit in the rewards box too, so that could have something to do with it. But I did manage to fix it by editing my save file! I'll post the steps here for anyone interested:
1. Install Notepad here:
https://notepad-plus-plus.org/downloads/v8.6.2/
2. Once you've installed Notepad, press the windows key and copy and paste this into the search bar: %AppData%\StardewValley\Saves\
3. Open that folder, then open the folder that has the name of your current farm
4. Open SaveGameInfo using Notepad, and search "craftingRecipes" using control + F
5. You'll see a bunch of strings of text for different crafting recipes. Find the string for wild seeds, it should look like this: <item><key><string>Wild Seeds (Sp)</string></key><value><int>0</int></value></item>
6. Directly in front of that string of text, paste this: <item><key><string>Ancient Seeds</string></key><value><int>1</int></value></item>
7. Save the file
8. Open the other file in the folder, which should be named after your farm. Ignore the files ending in "_old" - those are backups.
9. Search for "craftingRecipes" again, and put the string of text for ancient seeds in front of the text for wild seeds
10. Save the file, and load up the game. You should have the recipe now.