What are known 3SAT to 2SAT reductions?
Yes, there is.  Test whether the 3SAT formula is satisfiable or not.  If it is, convert it to the formula True.  If it is not, convert it to the formula False.  This can be done in exponential time, e.g., by trying all possible assignments, or by your favorite method for testing satisfiability of a 3SAT formula.

Under the strong exponential-time hypothesis, this is optimal: there is nothing faster.

In particular, any procedure for converting into an equisatisfiable 2SAT formula can be used to test satisfiability of 3SAT: first convert into an equisatisfiable 2SAT formula, then test the satisfiability of the corresponding 2SAT formula (can be done in linear time. This gives a method for testing the satisfiability of a 3SAT formula, whose running time is essentially the same as the running time of the conversion procedure.  Now the strong exponential-time hypothesis says that any method for testing satisfiability of 3SAT formulas requires exponential time.  It follows that any method for conversion also requires exponential time.