You can't learn to serve big consistently by swinging slowly, the different timing needed the different spin and trajectory required are completely different for a 100mph flat serve, a 80mph kick serve or a 70mph flat serve.
If I were to hit my second serve with just my arm it probably wouldn't reach the net, as the topspin would bring it straight into the floor without the upward and forward force imparted by the uncoiling of the legs and torso.
Equally, if you suddenly start using the whole body on a technique designed for slow sings, the ball will always go long, as the trajectory and timing will be wrong.
So while it helps to practice the elements separately, make sure you are practising to hit the type of serve you want to hit. If you are hitting with the right trajectory for an arm only serve, you are practising the wrong trajectory for a whole body serve.
One trick that works for some people, try practising the serve technique without a tennis ball or court. Focusing on the correct positioning and timing of the stages. This helps a lot of people with the timing of the kinetic chain, as it teaches you how the shot should feel. Then you try the exact same swing for real, and pay attention to how you are moving differently to the 'ideal' practice swings.
Also, I would recommend working on a technically simple, moderate pace kick serve first, then learn an extreme kick as a second, then learn the flat serve as a lower percentage variation serve.
Wilson 6.1 95s - 'If you call that a forehand I must have a fivehand'