Actually, everyone would need a partnership contract -- 90% of which would be more or less standardized, like the standardized Wills and Business Partnership agreements anyone can buy at OfficeMax for a few bucks.
And, just like Business Partnership agreements include pre-emptive clauses against Fraud, Embezzling, Malfeasance, etc., even the most basic "partnership contracts" would generally include clauses penalizing breach of Contract for -- at the very least -- the four "A"s (Adultery, Abuse, Addictions, Abandonment) statistically common to divorces with cause. You've just covered about 90% of the "Divorces for Cause" right there, and pre-emptively reduced the legal wrangling in case of dissolution (as the penalty terms for breach of Contract would be specified in advance).
Besides, your proposed solution opens the door to homosexual marriages anyhow, which is what we're trying to avoid!
No, if the State has no power to define a contract as a "marriage", then (by definition) no "partnership" could be legally required to be respected as a Marriage. Churches and Businesses could choose to recognize whichever "partnership contracts" they pleased, and not others, as the terms of a Private Contract are binding upon the Parties themselves, not parties external to the contract. State Law, on the other hand, is binding on Parties external to the contract, which is exactly why we are in this mess.
You're dreaming if you don't think that eventually state law would require all businesses to recognize and treat all "partnership contracts" equally, effectively creating homosexual marriage!