While I concur with the motivations behind your beliefs, you have failed to address one very fundamental problem: Accommodating polyamorous relationships does, indeed, require rewriting the marital code. There is simply no way that laws designed to give two people the right to share their lives and responsibilities together can be easily adapted to more.I probably painted Mormon fundamentalists with too broad a brush there. I wouldn't be surprised if there were a few Mormon polygamist families where 1. Marriage only happens in adulthood AND 2. There is no abuse. It is not because of polygamy that abuses happen, but because of patriarchal religious beliefs, which are a problem even in monogamous relationships.
You yourself cited a few examples where problems come in. Additional problems include who makes medical decisions for the other; who gets the pension and social security benefits when one dies; etc. Consider also a polyamorous relationship consisting of one woman whom several men share among themselves. We will assume for our purposes that each man is a Kinsey zero and has no sexual interest in any of the other husbands. What happens if the woman dies? Does the marriage survive her? Are these heterosexual men now condemned either to divorce one another or to live out their lives in a relationship that could never be sexually satisfying? Or should they put out a personal ad "Seven widowers seek suitable woman (or women) to become our new sexual partner?"
Of course one CAN devise solutions to every problem. But I have never seen anyone define a set of rules that would be desirable for every other polyamorous couple. Nor has any society practiced polygamy in a manner that treats each spouse as an equal. In Mormon society, in particular, the man holds all the power, and there is a hierarchy of authority among the wives. We have spent a century eliminating the male-dominated hierarchy in marriage law. Any form of polygamy that has ever been institutionalized on this planet would be a giant step backward from what we have achieved.