Can the application of logically equivalent “if-then” expressions in stimulus-response processes yield meaningful results? Can the application of logically equivalent “if-then” expressions in stimulus-response processes yield meaningful results in finding alternative stimulus-response paths, or do such expressions only describe the same path?

Not meaningful in general. "If I fly to the moon tonight then the Russians won World War II." is logically equivalent to "If I have 3 quarters then I have 75 cents." I have heard of a branch of logic called 'relevance logic' that does not allow such jibberish, but I have not personally explored it. You can probably construct a strong argument by writing your premises or antecedents and then stating what follows from them. It wouldn't be deductive, but it could be more powerful.