Your hypothesis is correct, about the strain reducing faster as the eye muscles recover more. However, it shouldn't encourage you to put your eyes through more stress. Think of it like a cut on your hand. As it recovers, it'll pain lesser when you poke it with a finger. But the more you poke it, the greater the chances are that the cut gets aggravated, and it'll take longer to heal.

I don't think your sleep duration could be related to how long you kept your eyes closed. It helps to write down or note down various details daily, in either a book or a text file on your phone. This will help you look back and correlate information when you perform experiments to see what worked and what didn't. Multiple experiments are required, keeping various variables in perspective, before coming to a conclusion.

As for the supplements, if that's what your doctor prescribed, perhaps it's ok for you to follow what the doctor says, but it's necessary to understand how exactly it helps, and verify it too. Else, it’d be a “belief in magic”, which I don’t encourage. There are many medical forums where other doctors might be able to provide an un-biased opinion. In my case, instead of obtaining nutrition from supplements, I would look for which foods provide that nutrition naturally, and make sure I consume those foods instead of purchasing supplements. That's why I emphasized on a well-balanced diet. My doctor said that the safer way to get nutrition is from natural food, rather than from supplements.

Very happy to hear that you are recovering :-)