Well, from what you are saying, your current diet sounds pretty dang good, compared to a lot of us

Have you just recently started eating this way, or just started, and wanting to go Paleo from there?
Paleo requires a lot of dedication. Since you have the health problems you do, if you have just started eating the healthy way you have already described, why not give that a chance FIRST to see how you do?
On the other hand; if you have these health problems, and have ALWAYS eaten healthy, and want to try Paleo, that's a different story.
PLUS, you say your current diet is very "clean". Maybe you need to look really close at it, to see if there are any ways to improve it, or things to try to eliminate to see if some of your health issues clear. When you say clean, do you mean that you do NOT: eat much sugar, preservatives, transfats, pre-packaged, etc.? Although from your post, it sounds like you do not.
I can relate to the Thyroid issues, as I've been Hypo for over 30 years. What kind of meds are you on for that? I can only comment if you are only on a T-4 med, you are not getting all you need for your thyroid to function properly. Armour is superior to anything around in my opinion, it has all you need, plus is natural to boot. But if you are on the Hypo end of the spectrum, you may already know that.