@Bassaur - a couple of thoughts:
First, you have a better shot of getting private disability benefits if you are older than younger. LTD insurers obviously are a bit more willing to pay a claim to a 50-year old than a 30-year old. You just represent a smaller hit to their bottom line.
Second, the fact that you have been sick for ~7 years and have stayed employed works in your favor, especially if there is a paper trail of medical records and doctor's notes showing that you sought treatment but haven't gotten better and kept working anyway. It's not fair to people who have sudden onset severe ME, but lawyers will tell you that it is easier to argue that someone who has been sick for a while has made a "heroic" effort to keep working while dealing with a chronic illness.
Third, speaking from experience, you don't want to keep working if your ME is going from bad to worse -- it's a really dangerous combination. I worked for 20 years full-time with ME, started to head downhill slowly about six years ago, then rapidly three years ago, dragging myself to work in a virtual stupor for about six months. I finally couldn't physically get to work starting in late 2018. I am now housebound with moderate/severe ME -- meaning I am still able to take a shower every day, yay! If I could do it all over again, I would accept the risk of financial stress, even poverty, over being severely ill -- in pain, exhausted, and unable to leave my homes for weeks/months at a time. Working as my ME got worse is probably the biggest mistake I have made in my life.
As far as advice about what steps to take:
First, you need to get a copy of your employer's disability insurance policy contract. This is the document that lays out the definition of disability, what exclusions apply, and what your monthly benefit would be. You don't want the plan summary but the actual contract, which is typically 30-60 pages long.
Second, you are going to want to talk to your doctor to let them know you cannot work any longer, that it is making you increasingly ill, and that you are having real trouble fulfilling your job functions. (Note: you don't want to risk being fired for poor performance, because if that happens you will no longer be covered by your employer's disability policy.) Hopefully, they will be supportive -- because they are going to be tasked with telling the insurance company why they believe you are too disabled to keep working. If they aren't supportive, look for another doctor.
Third, consult with a disability lawyer, one who has handled ME/CFS cases in the past. Don't hire a general private disability lawyer -- you need someone with experience with ME/CFS. A good lawyer will usually review your disability policy and have a free phone consult to review your situation. On the plus side, these lawyers have experience getting benefits for or winning lawsuits on behalf of ME patients. They also know what types of medical evidence (doctor's letters, statements, and notes, as well as testing) will support your disability claim. On the minus side, they can be quite expensive. Also, a lot of lawyers will tell you that a 2-day CPET is mandatory, though this is a grueling test that is ill-advised if you are already sick and heading down hill. One alternative is to get a neuropsychiatric evaluation, which is especially useful if you have cognitive issues, by a psychologist with experience with ME/CFS.
While I agree that it is a lot of work to win a private disability insurance claim, it is less effort than going to work. Also, a good disability lawyer can help with a lot of the administrative tasks, like obtaining medical records, helping you answer questionnaires, and interacting with the insurance company on your behalf.