When you practice your speaking "swing", you must start with mechanics: compose your sentence first word to period before expressing it; emphasize the period with a downward sound; etc. But you don't want to get stuck in a mechanical mindset. A great conversation or presentation is much more chemistry than mechanics.
Ultimately, mistakes, like saying um, are okay in small portions. Not being aware that you are making mistakes is the real problem. When these less desirable behaviors are left unchecked, they can get out of control and in the way of your listener getting your ideas. But it's both unreasonable and undesirable to expect technical perfection. You are human, not a robot. Your listeners want you to be human.
There is also a tension between being in control of sentence structure and being authentically expressive and dynamic. When I'm coaching my clients to speak in sentences from first word to period, to hit the period and to listen to their listeners with their eyes, they tend to flatten out. When I coach them to be more expressive, they tend to fragment sentences and/or omit periods and ramble.
There is a sweet spot, a sort of balance point that they reach after a lot of practice, in which they are slightly out of control of the sentence and genuinely expressive.
Key to all this is, of course, awareness. If you limit your awareness to the behaviors you are producing in order to be technically polished, you can't put your awareness on your listener. You can't observe them and absorb their body-language responses to you. You can't foster the chemistry that comes with being fully present with them. It's chemistry, not mechanics, that yields that immersive and memorable experience of listening to a great speaker.