You can surf the internet for a used one for your price range, or you can enjoy the journey of putting together your own .223 heavy-barreled trainer. More than your budget for sure, but if you pay as you go it is manageable. Bonus that there are no personal compromises if you do it the latter way.
I reused an old 700 action for mine. It wears a 26" Krieger heavy varmint, and is a joy to shoot.