Great question! Yes, the enemy ostrich will automatically flee and you may strike unopposed (but that won't count as unseating unless their Stamina is reduced to 0). I do like your 50/50 chance house rule though, and if it works for you I say keep it. As for chasing them down, that would also be up to you (and whatever makes the game more fun for you is best), but I'd probably do a Roll Under Ostrich Flying to see if I can catch up to them successfully.
You may be interested in a tactical jousting game I wrote, which is very much in beta and sorely needs more play testing. It's intended for two players but I've been playing it solo reasonably well. You can find it here:
https://drive.google.com/file/d/1JkTE__DCgGaMkP_4kJ0dsgsKaX6VPhtE/view?usp=share...
If you try it please let me know how it goes! Also happy to answer any questions about it as well.
And thank you for the compliments! It's good to know you're enjoying the game.