I'm not sure you can determine the reaction coefficients just from the activation energy values though. You can tell what the RDS is, but you can't tell how exactly the intermediates contribute. You would need, on top of that, a rate experiment where you measure the dependence of the rate on each intermediate.
You don't necessarily have two barriers there. Imagine this. E + S makes ESI, which also happens to be the transition state. Then the reaction flows downhill to the products E + P. That's elementary, assuming no intermediate steps occur in the active site.