how can I draw from a set of characters using a seed for entropy?
Yes, this strategy works, in the sense that it generates each character with the appropriate distribution, and there is not trivial attack (with the caveat that the formatting used must allow to unambiguously find $S$, $i$ and $c$ from the concatenation $S\|i\|c$; formatting $i$ and $c$ as fixed-width fields will do). However


We do not have a strong security argument: for this we'd need a MAC keyed by $S$, e.g. use $\operatorname{HMAC-SHA256}(S,i\|c)$; the HMAC construction turns a hash into a MAC, with a proof.
There is no entropy-stretching, nor salt, as in standard password-based key derivation; thus a guess of $S$ can be checked with low odds of errors knowing a password and it's $i$; if the seed string $S$ is low-entropy (like a master password), that's a huge problem.
We can obtain the appropriate distribution with far less hashes; see this.


Point 2 is by far the most worrying.