Preface: This is somewhat spontaneous and not thoroughly thought out.

If a couple freezes an embryo and then breaks up, who has custody/guardianship?

Given the legal precedent to privacy and ownership of our genetics, both parties ostensibly have ownership rights to the embryo (unless they were signed away for some reason). And I do think ownership is the more appropriate term here, rather than custody/guardianship, since common legal practice does not hold the embryo as a distinct human being.

If one party is willing to bring to term and the other isn't - who should win?

Given the ownership premise above, consent would need to be mutual.

Should one side have to take full responsibility, or should they still be entitled to child support, etc. from the other?

I would suggest that these terms be conditionally negotiated by the concerned parties as part of the process of establishing mutual consent. Child support should not necessarily be the default assumption.

Should one party be able to legally buy the other out, or buy themselves out?

I see no reason why the embryonic property ought not be subject to financial negotiation.

Each individual gets full legal rights to their genetic material. The fetus cannot be taken to term without the other person's concent.