If wont be hypo,buy hyperthyroidism. Like mentioned above,get a full thyroid panel as well as estrogens and insulin and adrenals(cortisol especially)

When you say paleoish,what exactly does a daily diet consist of?
You taking a good Multi ?Hows your Iodine intake? Boron also known to lower shbg.

I also did a keto diet for 8 months or so. I started carbs again too quickly which lowered my blood sugar too much(insulin sensitivity)
Went to a doc and got some test done.(He didnt know s**t BTW and this was an endo)
My free test was 92.4 pg/ml(ref range 35-155) and total test 713 ng/dl (250-1100)This was maybe two weeks after the re-indroduction of carbs. Come to think of it,I should have got my shbg tested just to see where it was at. Who knows what my free test was before the carbs. Insulin is known to lower shbg as well.

But I would address the root of course than throw drugs at it.

Edit: Found this thread and the root of his problem,glad he updated it
Skyhigh SHBG Levels - WHY?! | Page 3 | All Things Male Forum

One more thing,do you take flaxseed? I was taking flax daily and decided to get my test measure again,my Free test was lower by a wide margin . That was the only thing I was doing differently at that time and linked it to that. (This was after the above info)

Heres a study on that as well.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2752973/

I am extremely curious as to the root cause of this.