Should Ijust make more efforts and focus more to speak fluently?

Should Ijust make more efforts and focus more to speak fluently? I have a stutter of average intensity, without too many secondary behaviors, but present enough to make it difficult for me to start or finish each sentence. Speech therapy now focuses on accepting my stuttering coming, and I know it has helped me be more confident about myself and reduce (a looooooot) those secondary behaviors. However, I noticed that by concentrating, that is, speaking slowly, focusing on my mouth and speaking in syllables, I was the most fluent person in the world. My speech therapist advised me against this technique, telling me that it could exhaust me over time, and that's also what I said to some people when they got upset because of my stuttering (f*ck them btw), but speaking while accepting my stuttering also exhausts me in the same way? I still have to tell myself "let yourself stutter, don't force the words" etc., so I don't feel like I feel the difference in mental charge between the two. So should I follow my speech therapist or just focus on being fluent?