Sorry that this is such a long post, but I've tried to address many of the things you mentioned, and yours was a long post. Ha.
I am no doctor, just a fellow sufferer of long term back and neck problems. My spine problems are easy to detect on an MRI and some of this can be seen on X-rays, so I suppose I should count my blessings for that because at least I know my diagnosis and options for treatment.
But I don't think your own MRI results clearly identify which vertebra or disc is the most likely source of your pain or whether the pain originates from more than one source.
NOTE -- Please take the following with a grain of salt and don't consider it medical advice. I base the information only on my own experience and what I've read about back problems, from which I've suffered for years. For instance, I am comparing my own MRI results, which give a clear diagnosis, to yours, which I think do not clearly identify the main source of your pain.
You have several "abnormal" MRI findings, but I some of these are common to many people and result from the normal aging process. They do not always cause pain. This includes the degenerative changes and small osteophytes (bone spurs). Sometimes bone spurs do press on nerves and, in the upper spine, on the spinal cord. The compression of nerves or the spinal cord is often associated with "spinal stenosis," but your MRI results don't clearly note any stenosis.
Based on things I've read, your symptoms are those of a herniated disc that's pressing on a nerve -- pain that radiates to the legs and increases when sitting. Sometimes standing up relieves this type of pain. L1-L2 and L5-L6 are your most likely candidates for a herniated disc, I think, though your MRI results don't label L5-L6 as a herniation.
The Schmorl's node at L1-L2 is a "vertically" herniated disc (one that herniates above and below the disc, rather than outward). Apparently there is debate amongst doctors on whether these cause pain.
I don't think the "rudimentary" disc at L6-S1 would be considered a herniated disc, but maybe it could also cause these types of symptoms. It would definitely cause you pain, I think, especially if it's causing nerve compression or irritation or if there's "bone rubbing on bone" due to a virtually absent disc (one of my many problems).
Your difficulty walking could be a symptom of spinal stenosis, which can cause radiating leg pain like that of a herniated disc. But sitting often relieves the pain of spinal stenosis. However, spinal stenosis can result from a herniated disc so both problems may be present (as they are in my spine), and this could cause pain whether you sit or stand. I think L5-L6 is your biggest suspect for stenosis, because of the "decreased signal intensity" and bulging disc noted. I think this could indicate a compressed nerve. However, the term "stenosis" was not mentioned.
Spinal stenosis symptoms are usually not limited to pain, but will include such things as numbness, weakness, and other problems with the affected body parts.
Personally, I think the "decreased signal intensity" at L5-L6 is a particularly important finding, mainly because it has never been noted in my own MRI's. The MRI's of my neck showed several levels of nerve and spinal cord compression, and my lumbar spine MRI shows lots of very serious problems -- stenosis at two levels, a severely herniated disc, disc bulges and tears, a totally degraded disc, bone spurs, etc. (I'd love to trade for your own MRI.) Despite all of this, I don't remember any mention of decreased signal intensity.
If I were you, I would not rush into having back surgery unless your doctors are certain which of your vertebrae are causing the problem. It seems that several levels of your spine are potentially the source of your pain, if it does indeed originate in your spine. I doubt that you'd want to fuse your entire lumbar spine just to make sure you fixed the "bad" disc, and most likely you can't find a doctor who would do that.
If you rush into surgery, you might end up being one of those people who continues to have problems despite surgery. Once a section of your back is fused, it puts stress on the other vertebrae and makes them more prone to developing problems. So if the "wrong" vertebrae gets fused, it could increase your symptoms rather than relieve them.
It's my understanding that back surgery, especially fusion, is very major surgery that requires a long recovery period and may not fully relieve pain; i.e., you shouldn't take it lightly nor do it unless your symptoms cause severe limitations of your activity level or if your problem threatens to paralyze you. But if you are offered a much less radical surgery than fusion, perhaps it's worth a try.
Exploratory surgery may be helpful for some types of illnesses, but I definitely don't think surgery should be used as a diagnostic tool for back problems.
I myself will soon undergo a multi-level fusion of my lumbar spine and have already had a multi-level fusion of my cervical spine that succeeded in relieving most (but not all) of the symptoms related to my neck. I do not expect relief of all pain after the back surgery, but am hoping only for improvement that allows me to "have a life." My back problems currently make it very difficult to perform even the most routine of tasks, such as grocery shopping and house cleaning. My doctors have different opinions on whether my severe nerve compression threatens to paralyze me, but I think this is indeed a risk, so I am opting for surgery.
But my suggestion to you is that you first try "conservative" treatment such as physical therapy that includes moist heat and electrical stimulation therapy, or perhaps traction. Injections might also help. Even my own severe problems produce less pain after a few sessions of physical therapy. I also get some relief from ice packs and a moist heating pad. Another option is a stimulator device that you wear each day. Perhaps you should consult a pain specialist to try out various methods of pain relief.
Back pain can build on itself because it produces muscle spasms that in turn produce more pain. So it might be helpful to try a round of muscle relaxants, perhaps combined with pain meds (I take this combination).
Some people can obtain relief from NSAID over-the-counter pain meds, but they don't work for me. However, there are quite a few alternatives to opioid pain drugs, if you're hesitant to take them. For example, some people use Lyrica, Neurontin, or Cymbalta for chronic pain. Tramadol is another pain med considered less drastic than opioids such as Vicodin. Have you explored all these possibilities?
I had terrible pain for 7 years, then they removed my prolapsed uterus and pain went with it. Could it be that for you?