@ChickenCanoe probably has more experience with chickens than all of us put together as he is an instructor and knows what he is talking about. I have used the elevated cage method with good results and found that it generally takes about three days. I did take a shortcut this summer with one of my persistently broody BOs. I cooled off her breast muscles and nether regions with a bath in a cool pool, which she seemed to enjoy, before putting her into the cage. I repeated it the following day and then released her to forage with the flock. She did not return to her broody nest. I used that method again on a different hen, also a BO, with similar results. These three-year old BO and a third one kept going broody, however, and I eventually culled them for the freezer.A broody hen wants to sit quietly in a trance and for the most part, doesn't experience stress during the cooling period.
We used to keep 100 leghorns in a large henhouse with a high roof. We always had about 3 homemade cages hanging from the cieling of the henhouse. It seemed like there were always a couple hens, give or take, serving jail time. They never seemed stressed and none that I have had elevated in the years since ever exhibited much stress till they were cured and started pacing.
You are fortunate that removing eggs has worked for you. I've never experienced that. They usually just continue to sit patiently awaiting one of their flockmates to give them more eggs.
Perhaps she wasn't that dedicated to the process in the first place.