Since it already is a good converting page, why don’t you try A/B testing on it? (let the original version stay put and go about making changes in the new variation page and target it to the specific set of audience).
See if the variations convert better than the control version. If yes, make the variation the original version and repeat the cycle yet again.
To know when, for how many visitors, how long an experiment should run, and for how much audience, use this A/B testing calculator.