When I first filed for LTD, my insurer ok'd it, but after about 18 months claimed that I could return to work. Their assessment was based on their doctors, none of whom had ever talked to me or examined me. I did have to file an ERISA lawsuit against them, which I eventually won. If you happen to be CA, send me a message, and I'll give you the law office's name.
Fatigue is a tough one to document. But here's some ideas. First, get a copy of your medical records (you can get them directly from your various doctors). Since you are doing adderall, you've been to some doctor, you've said you've had problems with fatigue, and the doctor's records will document that!
Whenever you are filling out forms, don't be general, be specific. Don't say "I get tired easily". Say, I get up a 6 AM, go to work. After my drive to work, I sit and rest in cafeteria for about 15 minutes, as I find focusing on driving draining. I review my tasks for the day, and am productive til about 10 AM when I need a break to clear my head. I find constant interruptions hard, which didn't use to be a problem for me. (Obviously I'm making this up, but you get the idea) Continue through the highs and lows of your day. Also any details around home, like my son now mows the grass, and my wife does the groceries, both of which I use to do. On the weekends I take long naps, which help me recover somewhat from the work week.
If you've had any complaints from work about your performance, which used to be good, worth mentioning.
The functional testing can be useful. My lawyer in the ERISA suit sent me to functional testing. I spent two days in the testing, which touched on a variety of tasks, from physical things like stacking objects and carrying relatively light loads (5-10 pounds) to math tests and word processing and writing. They tend to customize the testing based on your occupation. I was deeply embarrassed by the math tests, as my background was as a software developer, and I tested out at 10th grade level, with lots of basic errors. Part of my short term memory issues! I also had a meltdown on the second day, as I was so tired at working and pushing that hard on the tests (I'm one of those folks who always wants an A), that I was just exhausted by about 2 PM on the second day. My former employer certainly wouldn't have wanted me in the tired weepy phase I was in.
The appeals process is long, and complicated. But it's worth doing. If you are 57, Medicare won't kick in for another 10 years. Getting a part of your salary for those 10 years is going to make a big difference in your finances. You may also consider whether you should consider whether you should apply for Medicare disability. If approved, you will get Medicare health benefits 2 years after the date they think you became disabled. Which does two things: gives you insurance, and points out that if Medicare things you are disabled, it's a bit odd that your insurer doesn't. (Typically Medicare standards for disability are higher, but they "get" that older people become disabled for health reasons.)