I'm not an expert like some of the guys here but it seems like your attempt to generate more ball speed is causing you to walk faster during your approach. This is causing a timing issue, which is the reason your arm is not going where you want it to go.
I don't see an issue with a slow ball speed as long as you are using the correct ball for the lane conditions and the ball still has energy when it hits the pins.
Tell us more about a typical league night. Do you score the best when the lanes have fresh oil? Due to the slow ball speed does your ball over hook when they break down causing your scores to drop and make it difficult to make spares?
One of the first things you should strive for is to develop consistency on the first shot. This should leave easier spares to shoot at. Next on the list is, convert more spares.
Consider buying some books on bowling. I just finished Jowdy's Bowling Execution
and Hinitz's Focused on Bowling. These tow books would be a big help to someone looking to improve the physical and mental aspects of bowling.
If a picture is worth a thousand words, a video posted here is worth several pages of practical advice.
Get a friend to help you record a rear view and side view video of your approach and ball as it moves down the lane. It will be helpful if we can see your basic style and what happens when you try to speed things up. Post these on youtube and put the links on the appropriate board. The guys here are very helpful and knowledgeable.
Good luck with improving your bowling scores.