I'm the same. Even though it's counter intuitive to how you usually try to say it. I find if I breath out and start the word half way through the breath even if it feels weird to start a "t" sound or other hard start syllables like the ones you mentioned mid breath, I find it smoothes the start and eventually you can do it well enough it doesn't sound noticeably different. Once you get used to it it. You'll have less anxiety about it then it'll get even easier. My stutter is very anxiety related so anything that reduces the anxiousness around my speech the better I am. I hope it helps you too.