Slight improvement could be to have the input using a key-spend level adaptor signature instead to late-bind R to secret. Then the output can simply be going to S, since there is no need for for the Alice clause (she got her secret already).
This would turn the secret hash into a curve point, so for maximal savings you’d have the leaf policy in the new tree also be a key-level adaptor spend rather than a tapscript hash image reveal, leaking the same secret.
Alternatively with CSFS, the secret can be late-bound via a single Alice CSFS based signature, which can leave the secret hash-based.