Not much more to it than to slow down the part that is challenging you to a tempo where you can play it perfectly, with confidence and conviction. It doesn’t matter how embarrassingly slow that is to start with. Important thing is to be able to play it right - consistently, every time. The brain considers mistakes a learning experience so perfect practice is the best way to practice here. Then you slowly move the tempo up to where the song actually is and you’ve got it. The sort of work won’t bear fruit overnight or even over a week’s time but it will happen.
Getting this stuff clean and smooth comes from doing the reps. There isn’t really a hack for it. If you’re happy and comfortable with your finger style playing, you have to remember how you got there. You got there through reps and doing it over and over and over again on a regular basis. Same thing applies to pick playing.
The other thing to consider is consistency in your physical approach. choose a pick style, material, and thickness that you like and stick with it. It’s tough to get any of this together with the goalposts always changing. You’re also want to pay attention to how you hold the pick and make sure it’s the same all the time. Finally, it may feel more comfortable to play the material close to the bridge, or maybe a little farther away from it. Whatever that is, find a spot and also just stick with it for consistency.