After spending numerous hours researching and troubleshooting possible solutions, I came across one that worked for me and might work for anyone else experiencing this issue.
For whatever reason, the Vulkan Graphics API is incredibly unstable and can create some issues, such as the one described in the post above. Swapping from Vulkan to DirectX 12 fixed the problem for me and prevented my keyboard from disabling once loaded into the game.
To whoever's reading this, I hope this works for you, as it did for me, and that you're saved from having to go through the same frustrating process as I have.