Sport shots will force you to be more precise with your shots. Going back to house, you realize just how much more forgiving they are. Kinda like practicing 6’ putts all day then doubling the size of the hole and seeing if you can make it.

Besides the new ball, maybe consider a lesson or two from a good coach. It’s helped my son tremendously. Especially of late. He’s finally grasped the difference in getting his hand through the ball instead of rotating around it. Strike percentage has gone up 10+% in the two weeks since that light turned on for him. Still hasn’t fully integrated it yet either. Too much end of year stuff with his team and season to solely concentrate on it.

It could be something you’re not aware of that is an easy type fix. Trained eyes see tons.

A change here or there can help with carry as well with your confidence with angles.

Your game sound exactly like mine.  On THS, I like playing up the outside and the inside isn't a favorable spot (but its getting better).

Do you know the name of the pattern(s) that you will be bowling on?

If you do, then research the pattern (Google & YouTube, etc) and see what the general strategy is.  That can help a lot because maybe you are playing the pattern wrong (done that before).

Credit to OP for going in the deep water.  It will only serve you better in the long term.

Only a few of the things I would emphasize:
-Have a well rounded arsenal but definitely focus on getting a variety of different shapes in the bag 
-MOVE THOSE FEET!
-EMBRACE getting out of your comfort zone.  If playing the twig is scary, do it!  If you're afraid of a nosebleed but the shot is telling you 5th arrow and to get around it, do it!  FIND A WAY!
-Don't focus on score as much as focus on getting better every session at something.  For me I'm always seeking to anticipate transition and filling frames.  One summer long ago it was the opportunity for me to throw plastic at all non-sleeper (except the bucket) leaves.  That has had a lasting impact on my game, scoring and has generally simplified everything in my spare game. 

Agreed with the above posts... I'm 46 now, but was blessed with 4 years of collegiate bowling that taught me all angles, and I'm very limited in rev rate and a up the back of the ball style that lends to down and in, but I love playing the gutter when I can and can handle deeper angles when necessary, it just comes from practice and experience.  And kudos to being in the sport league, we need more bowlers like you.  I only have time for one league these days, and I choose a sport league.

On the D/S Open pattern... it was tight in the middle to start and forced the majority right to start, our crankers played 10-11 board out to 6-7... I played straight up 4-5 board the majority of the time.  However, at the Open, you work together to break down the shot (or should).  In league, it's just a different atmosphere and if you aren't consciously working on the pattern together, it could get much more difficult than it needs to be.

Arsenal... sadly I think, if you aren't a versatile released higher average bowler, more balls are needed to cover more conditions.  I'm higher averaged, but not versatile with my release.  For sport shots I have a Paradox, IQ Tour, Match Solid (polished), all with 3-4" pin to PAPs.  House shots, the Honey Badger, Crux Pearl, Hyper Cell Fused all with 4.5-6" pins are preferred for me.  I would say my Jackal Ghost is another strong option that goes with me everywhere.  I've loved my Honey Badger on all conditions so far and am punching up a Honey Badger Claw and White Hot Badger that I hope will make both the sport and house bag.

I think a Prime would suit you well... but if you like your Turmoil Solid at the current surface, maybe getting another strong solid symmetrical drilled to compliment that would be worth it, Eon Infinite, Web Tour, Intel, IQ Tour all come to mind.