If your hypothyroidism is due to autoimmune thyroiditis ( and it likely is) kelp can make it worse.
Just give the Synthroid a try. Hypo is generally not very complicated.
Nothing is a cure. It doesn't get cured it only gets controlled.
No! I would not suggest that. No way to regulate levels.
Further more, Doctor probably wouldn't monitor you, then how would you know what your levels are, to know which direction you need to go with your levels, i.e., if you need to reduce or add more supplement.
There is help out there for medication cost, either low cost or free. TV talk host Montel Williams advocates such a program. Medical and payments can be worked out with the doctors billing department. So there is no excuse for taking matters as medical into your own hands, risking your health and life.
Don't risk your life or health - its not worth the money saved, if fact it just may cost you more in the long run.