The snagging could be due to the way you bind. Are you making a large loop? (I just want to help)
Also, what weight do you prefer?
If you like heavy yoyos and dead unresponsiveness, I would look into the New Breed, Legacy or Atmosphere.
If you like heavy yoyos and slightly adjustable unresponsiveness (still responsive but easier to bind for your level). I suggest the Dark Magic.
Those are the only yoyos that seem to fit your price and preferences.
I personally think that with your level of binding, the Dark Magic is best for you. But if you want to REALLY practice your binds and not be fully able to bind for a few days on the dead unresponsive yoyos, I would say the New Breed.
Please note that all of these yoyos will get you to any level you want.
Also, it is time to clean the bearing if it starts getting responsive even with the proper amount of thin lube. (Too much will make it responsive) I would suggest cleaning your bearing every 3 to 5 months. Just note that the more you clean your bearing, the less life it has. It’s a trade off between performance and longevity of the bearing. (Really, if you clean it every 3 to 5 months, the bearing will last you long enough for it’s money’s worth and more.