I have to admit, . When I first started to read your post, I thought, "sounds kind of like narcolepsy or some other sleep disorder", but your last paragraph cleared that up! I think it was smart of you to get a sleep study done, to rule out sleep apnea and narcolepsy.
I'm glad you take measures to not burn yourself with your tea, as that would be even more unpleasant than waking up with a warm, wet lap (which, also sounds unpleasant).
I know many of our members have shared stories of their bone deep, unrelenting fatigue, so you are definitely not alone in that! One of our contributors wrote about how MS can feel like narcolepsy -- https://multiplesclerosis.net/living-with-ms/narcolepsy. And here's another piece she wrote on daytime sleepiness -- https://multiplesclerosis.net/living-with-ms/tired-all-the-time-is-it-sleepiness-or-is-it-fatigue. There are literally a dozen or more stories/articles on the topic of sleep and MS on this site, so you find yourself in good company!
Now, as far as dealing with the sleepiness? Well, that's another issue. Some of our members have had some measure of success improving their sleep, while many others have learned to live with the fatigue and manage their daily lives around it, when possible. Some members have prescriptions for a medication called Provigil, to help with the fatigue. But, using it to treat MS symptoms is considered off label use and many insurance companies won't cover the cost of it for that reason.
I would definitely keep in communication with your doctor about any underlying causes (besides MS) and make note of any more changes to your energy/fatigue levels.
As I said before, you're definitely not alone in this!
Best, Erin, Team Member.