Hyperactive language critic checking in

Saw this billboard, an ad for Cream O’ Weber Dairy, somewhere in the vicinity of Salt Lake City:

Milk it for all it’s worth

I spent, I kid you not, at least a couple of hours of mental energy in the ensuing three days going back and forth over whether the “it’s” is the kind of mis-use of the apostrophe that drives me crazy. There’s a bumper sticker that I used to see all the time in Tucson, that proclaimed a radio station to be “Worth it’s weight in gold.” Maddening. Contraction versus pronoun possessive, it’s not that hard, people.

But this dairy billboard has something going for it either way, and some unproductively OCD piece of my brain is still thinking about it. So, I hereby invoke the lazy web, or at least the portion of it immersed in English language idioms, to help me figure out the level of grammar scorn I should be applying. At issue is the meaning of the idea of milking for worth.

Option number 1 is that the phrase is intended to mean “milk it for all that it is worth,” which would clearly be contracted to “milk it for all it’s worth,” but with which I have some discomfort. Option number 2 is that that the phrase is “milk it for all the worth that is possesses,” which is clearly not subject to a contraction, and in which case the billboard should read “Milk it for all its worth.” My own leaning is for number 2, because it seems less cumbersome to me. But I’m weird that way.

So, voting is open. Is there an etymological tradition that should rule here, something that could establish the actual origin of the phrase? If not, I’m open to a democratic process.