The larger the transfer of rights, the more it demands of the state to enforce it. You cannot have maximal contracts maximally enforced by a minimal state.

I disagree about this. There is a stable equilibrium in which the state is known to be fast, effective, reliable, and uncompromising in enforcing the rules, and in which transgressions are consequently extremely rare (and swiftly punished when they occur), so that the resources devoted to judiciary and law enforcement can be very small. Such an equilibrium in which little enforcement effort is necessary in practice is possible with contracts too, not just with criminal law.

(In fact, large resources devoted to law enforcement are usually a sign of the state's weakness, not strength. They indicate widespread law-breaking, which in turn indicates that a lot of people are in a position where it seems like they can get away with it -- and the state is, for whatever reason, incapable of making law enforcement more effective and pushing things towards the above described equilibrium, and instead responds by throwing more resources into the existing ineffective system.)

Contracts are very rarely enforced, in the literal sense of forcing the parties to carry out their promises. (Joining the army is the only common exception.)

That's not completely true. Specific performance orders are given by courts in other kinds of cases too, typically when the contract is about something unique, i.e. when the exact same thing can't be obtained elsewhere, like a piece of land or an artwork. (In other cases, such an order wouldn't be in the plaintiff's interest anyway, since the defendant would presumably provide the worst quality work/goods he could get away with.)

To some degree, you can even stipulate specific performance in case of breach, although I have no idea to what degree this is enforceable in different jurisdictions.

On the other hand, regarding this:

That a contract literally transfers the rights stated in the contract from one person to another is in fact not what a contract is, at least in Western society. [...] In ordinary, non-libertarian states, all you risk by failing to perform on a contract is your assets and reputation. Your rights in your person are generally not transferable by any contract. That they should be seems a strange thing for a libertarian to be arguing for.

This is basically a question of definition. If you insist on using the name "contract" only for those contracts that are enforceable in today's Western societies, fair enough. However, the following must be taken into account:

1. The limitation that your rights in your person are not transferable by contract is just one example of the limitations I was mentioning. This limitation didn't exist (or was far weaker) even historically in Western societies, let alone in others.

2. This limitation, while seemingly reducing to a simple statement, is by no means straightforward when you consider its implications in practice. For example, what exact types of marriage contracts would be implicitly disallowed by it? Trying to answer that question leads immediately to deep ideological clashes.

3. This limitation, even under the broadest interpretation, is by no means the only one that exists in modern Western societies, both with regards to marriage and all other voluntary arrangements.

4. Finally, however you turn it, this limitation is ultimately a limitation on freedom. If I'm forbidden to sell my car, this diminishes my rights in my car; similarly, if I'm forbidden to sell myself into slavery, this diminishes my rights in my person. This conclusion is very unpleasant for libertarians, but the fact is that a libertarian must make some sort of unprincipled exception to libertarian principles to disallow slavery contracts. (There is a very well written article titled "The Libertarian Case for Slavery," which was intended as satire, but there's absolutely nothing in it, save for the sneer in its last sentence, that is not perfectly logical and valid reasoning from libertarian principles.)

(Of course, it may be that for game-theoretic reasons, such limitations on freedom ultimately increase total freedom by some reasonable measure -- "freedom may be freedom to capitulate," as Schelling says. But once you admit exceptions to libertarian principles on these grounds, the slope is very slippery and steep.)