iterations of a $\epsilon$-FSM transducer on a tape as equivalent to a TM computation
Yes, it is a lovely observation. At first it might be a little surprising, but it is widely known, in disguise.

If we write the instantaneous description of a Turing machine as $vqw$, where $q$ is the state, $v,w$ are the segments left and right of the head, then the next ID of the TM is obtained by just a local transformation of the string $vqw$ (namely $q$, the letter next to $q$ that the TM is reading, and one or two neighbouring letters). This observation is used when showing that every TM accepted language can be generated by a type-0 grammar. Such a grammar can only transform a local part of the string (and thus this can be simulated by a FST/GSM). Applying consecutive derivation steps then is iterating the transducer.