Spiriva is extremely drying and it will make for thick mucus that is hard to cough up. Advair is also drying and I note that your extremely high dose of that inhaled steroid is not generally recommended.
I got rid of Spiriva because it was drying. It didn't help anyway. I got rid of Advair because I developed adrenal fatigue, osteoporosis, and it gave me a hacking cough which exhausted me and could not have been good for my lungs.
I was put on nebulized Mucomyst (in addition to nebulized Duoneb) and for the first time in years my lungs were clear of phlegm - totally clear. No more choking myself to exhaustion. However for some reason this is no longer on the market (this may be temporary). However what you can do is take an over-the-counter mucolitic. The only worthwhile one is Guaifenesin. You don't want to get Mucinex which has other ingredients, but plain guaifenesin. Also, take 500 mg of vitamin B5. That is also a mucolytic. No side effects.
Are you seeing a family doctor or a lung MD?
A note about your phlegm problems. From using the emphysema medications one can develop thrush (a fungal infection). This no doubt extends to the lungs. Antibiotics and prednisone are marvelous food for fungi. They love it. So what do you do to help yourself....
Mucomyst is back on the market. That will dissolve the phlegm and has a neutral ph, unlike stuff like Spiriva which is acid. (Fungi thrive in an acid environment.) Also you might want to take a potassium iodide supplement. That will help, and oil of oregano will go after fungi with a vengeance. Usually the culprit is Candida albicans.
I have been on a steroid inhaler for the past three DECADES, since I was 29. Recently, I stopped eating bread, and never had to use my inhaler again. Have not used it since. A couple of nights ago, while eating out, I did eat bread and way too much...later that night my tight chest and wheezing was back. I will not be eating any more bread or anything with gluten. Also, did you know that milk and dairy products increase phlegm? They do. I stopped milk about 6 months ago, which also helped me get off the Advair. Good luck to you.