Ditto Newport's suggestion of alpha lipoic acid. I've seen the suggestion that high reverse T3 can be the result of heavy metal toxicity, in addition to low ferritin and high/low cortisol. Taking any thyroid product with T4 in it will worsen the reverse T3. You'll be looking at taking T3 by itself. With heavy metals involved, you'll have to be careful not to overwhelm your detox system by pushing metabolism higher than liver and adrenals can handle.
Keep plugging away at the iodine. My husband had to take just the SSKI, for the same reasons. He would periodically get swamped by detox, and need to take breaks to detox thoroughly before resuming iodine.
If you haven't already visited Stop the Thyroid Madness, you're due. Lowering reverse T3 is no picnic. (This link causes Microsoft to need to send an error report, then the page loads. This is a recent problem with the site.)