This is something that I have struggled with for many years, as I had some ANTs that just seemed too tough to deal with. However, you can break them down (as I was able to finally do), by doing the therapy consistently and using the strategies from it. You are correct in that it will take time and patience by chipping away at the anxiety pathways, and to create the new, rational pathways.
There might be some situations that are just too overwhelming for you to handle at this point. To continue to break down the ANTs that make you feel this way, you can work on keeping your mind open and going conditional with your thinking, by saying statements such as: "maybe this situation isn't as difficult or challenging as it seems to be right now...maybe in the future this situation will not be as bad, maybe it will be even less difficult next time". Something like that will get your mind to open up a little bit more, even if it still feels like these situations seem to tough to deal with at the moment.
Just keep moving forward and eventually you'll be able to weaken these ANTs.