But property, as a concept and related body of law, exists for the benefit of society—we tacitly agree not to take each other's stuff because lacking that rule would suck for (most of) us.

Intellectual property as a concept is a recent attempt to recast things like copyrights, trademarks, and patents—government granted monopolies intended to serve specific purposes, and tolerated for the benefit of society—as some sort of Lockean natural right.

However, if you are trying to reconcile the two concepts, you must face the fact that intellectual property restricts each of us from full enjoyment of our actual property.

(For instance, I can't lawfully use my own computer to copy someone else's copyrighted book, my garage-full of parts to implement someone else's patented invention, or even my own pens and paper to market products under someone else's registered trademark.)

"Manag[ing] it contractually", as you put it, would prevent this from being a problem. (Whether an opt-in scheme would be very effective is another story). However, this position relies on the right to contract, not any inherent right to intellectual property, contrary to what your earlier post implied.