Given that this is built on Ironsworn, you could use that for combat. The base Ironsworn game is free to download.
There is the problem of the monster catching mechanic though... You could maybe emulate the catching mechanics in Animon or Monster Care Squad? Those are paid TTRPGs. Some free ones I'm finding on Itch.io are Ligmamon and Pocket Monsters Manual.
IDK, just throwing some ideas out. I might be a little more comfortable frankensteining my own systems than you are though. 😅