It sounds like maybe you are someone who should try the alternative type of thyroid med, natural desiccated thyroid. If you're interested, you could try looking at the website "Stop the Thyroid Madness", which deals with the failure of conventional thyroid meds. They also have info on their website which will help you find a doctor.
Clearly, the results you've gotten from conventional, mainstream medicine have been unsatisfactory.
Also, maybe the paleo diet isn't right for you. You might consider doing a raw diet, and seeing if there is any improvement. You're problems may have to do with sluggish digestion, and meat and paleo foods can be hard to digest. I know, because I've done the paleo diet before.