How can the Schmidt–Samoa cryptosystem uniquely decrypt large messages? Suppose I choose $p=7$ and $q=11$. 

This gives a public key of $p^2·q = 539$.

However, decryption occurs using a modulus of $p·q=77$.

If a person chooses to encrypt $500$ using my public key, how do I recover this value if the decryption modulus is so much smaller?

Is this a limitation of the Schmidt-Samoa scheme? 

Is there a maximum message size for this scheme? How can this size be securely provided to the user without leaking information about the private key?
When you take a look at the paper you can see, that it is actually defined as a key-encapsulation mechanism, meaning that you will never encrypt data, but only keys for a symmetric encryption scheme. (That is, short messages.)

Further in $\mathsf{TKEM.Key}(pk)$ the "key carrier" that will be encrypted is explicitely chosen from $\{0, 1,\ldots, 2^{rLen} - 1\}$ where $rLen = 2k − 2$.
As $p$ and $q$ are both $k$-bit primes, $pq$ will always be greater then $2^{rLen} - 1$ and therefore the problem will not arise.

If you view the scheme as a public key encryption scheme, then the message space is simply $\{0, 1,\ldots, 2^{rLen} - 1\}$. You are not supposed to encrypt larger messages. (which is fine, because $k$ is a lot larger than in your example and you only want to encrypt short keys.)