This is not similar to my proposition of using the notion of velocity of money?
Your S==1 is the same of 
is constant.
And my 
= your MB/SC
And
if (TA > A) { //fewer SafeCoins have been absorbed than we want
MB/SC–; //So increase the PUT price to start absorbing more of them
} else if (TA < A) { //More SafeCoins have been absorbed than we want
MB/SC++; //So decrease the PUT price to start absorbing less of them
}
is
If T (quantity of PUTs) increase P should decrease for that we increase M (total safecoin).
If T (quantity of PUTs) decrease P must increase, so we diminish M (total safecoin).
The M is controlled via the rate reward.