Forward error correction with limited possible errors
Reed-Solomon codes are perfectly matched to a symmetric channel for which the probability that a given symbol $X$ is changed to a symbol $Y \neq X$ is the same for all choices of $Y \neq X$. That is, no particular symbol error is more likely than any other symbol error.

Thus, knowing that the channel is not symmetric and that certain symbol errors are impossible doesn't help in the decoding process at all. This knowledge might be usable in the post-decoder processing. If the decoder has corrected $Y$ into $X$ and $Y \notin S(X)$, then that is a dead giveaway that something is awry, right? So, the post-decoding processor can reject such purported "correct decoding" and ask for a retransmission or blank out that codeword to produce a blank area on the screen instead of gobbledygook. 

Unfortunately, the most likely problem with Reed-Solomon decoders is not that they find an incorrect codeword, but rather that they fail to decode because the received word is not at Hamming distance $t$ or less from any codeword.

I don't think you are going to find any way of increasing the rate of the code based on your knowledge of the channel's asymmetry.