Your scores should not be a response to the caliber of your competition. If you can average 200 then you should be able to do it no matter if your competition averages 150 or 250. It is all about you, you need to focus on your game, your opponent doesn't have any say in how you bowl, but if your opponent is bowling bad and you don't put them away and start missing easy spares then that is you not focusing on your game.
That is the main reason why many people don't make it on tour because their opponent misses a shot and they don't have the stones to focus on their own game and put the game away, they see an opening and decide they can take it easy this game is in the bag, meanwhile their opponent sees an opening and strikes out to win the game. The point is stop being lazy and make the shot. I would suggest that you don't need to move on to the more competitive league unless you can average 190 or better. Remember you are the competition not your opponent.
Something my coach has told me, a lot! Even when he brought in a pro for me to bowl against I heard "if you give him an opening he'll close the door on you!" LOL and I did just that. Though it was an interesting challenge for my mental game. Now I just do what my abilities allow, and I encourage my teammates as well as the opposing teams. If the opponent is cleaning up frames I know I can't do anything about it, besides do my job and follow suit.