Sorry for your pain. I have a very engineering based simplistic view of the body also some significant interest due to family member with major spinal injury. I am very optimistic that you can find a solution, but it will require time.
Here is my 2c worth -> a trial "model"/hypothesis based on an understanding of an explanation of the spine like
Lumbar Pinched Nerve, Physical Therapy, New Jersey, NJ
(1) A nerve is getting pinched when you sit... and now lie probably due to continual pinching causing inflammation and exacerbating the pinching.
(2) The areas of numbness (buttocks and backs of thighs) almost tell you exactly what part of the spine. Seems lower down and this why it might be difficult to work out a position as you have more flex a few vertebrae higher. However, there may be more than one area.
(3) It is not getting pinched when you exercise - sounds great that you can find such a position(s).
(4) Having it pinched makes it inflamed and easier to pinch
(5) At the moment anything that hurts is bad, so don't do it -> increasing inflammation
(6) If you can reduce inflammation and maintain it in a state that the nerve is not pinched, the right exercise may help your muscles to maintain that state (but exercise may or may not be sufficient) - I know fusion/rods/screws can provide completely pain free mechanical replacement of
major (think missing chunks) vertebrae damage.
(7) So if the above is correct then I think it makes sense that step 1. Stop inflaming it: Find a position when you lie down that does not hurt and keep yourself there when asleep - use pillows? brace? zero gravity chair?
relax the back chair? I am thinking that if you can find it while standing and exercising that it is possible.
(8) I can understand MRI not showing. The anti-inflammatories by mouth are prob not strong enough when you are really inflamed; Steroids etc reduce inflammation, if they get it in the right spot - L4 and L5 seems too high for your current pain. It may be that you have damage in a couple of areas
Also you had an underlying issue... before continual pinching inflamed it... so reducing the inflammation will not necessarily be a 100% fix.
(9) Unfortunately, this stuff takes time to fix and diagnosis can be slow. e.g. in our family case damage to nerve took months to heal completely, even though source of damage/pressure was 100% removed by surgery... and you are constantly inflaming it.
(10) I don't think I read anything in your description that does not fit the above framework. Obviously the above is not medical advice and I think you should persevere with finding the right spinal/nuero guy or gal.
However, I hope this simplistic framework helps. If you can describe exactly what spinal positions hurt and what doesn't this will help in conversation with medical profession.