Lots of detailed comments, but let me just make two suggestions that are more 'feeling' oriented.
Firstly, I dont think the way you're practicing the serve is going to yield rewards. The serve is a very intentional shot, and knocking out balls quickly is going to train that. Make each practice ball deliberate - this includes the transition forward. Basically, each ball should be practiced as a complete serve. Make it VERY intentional and focus intensely on that one ball - just like in a match.
Second is a technique tip. It really helped me to imagine that I'm leaning into the court - so as I prepare my left hand to bounce the ball down, my right hand goes up past my own head. This helps with weight transfer, but also with racquet prep and rotation - so almost imagine your two shoulders are coupled with a steel rod, and as you move your ball hand down, your racquet hand has to come up. Try it - maybe not your thing, but its something I still use to help my serve technique.