We don't know how much of either you'd apply, if you mean using as directed then you'd be putting too much fertilizer on in total by changing from a 3 week to a 2 week interval using the same amounts.
I am not convinced that adding some synthetics (a conservative amount) necessarily "destroys the soil web", but the amount and frequency of (any type of) fertilizer depends on several variables, you can either continually get your soil retested or make observations about how the plants are responding. Anything in excess can be bad but I see no evidence at all that my plants are worse off for having both organic and synthetic nutrient sources. Farmers have been doing this for decades using manure plus synthetic fertilizer with great success so long as they don't overdo it (large scale environmental issues aside).
Overall, if you give a plant enough supplimental nutrients to get as big, as fast as it can, then you run out of room in a pot and have to water more often. If not in a pot or using a very large pot, you can amend the soil with compost and easily broken down organic matter as the primary nutrient source (in addition to the soil itself), and can more effectively fertilize at 1/4th the directed quantity but twice as often (so averaging a half dose, or a quarter dose of each when using two different fertilizers).
Here's the question Randy: How are the plants doing? If you are happy with the results, the cost, and the time spent the way you are doing it, then rather than large changes you are needing only minor adjustments in method if any. However being in Florida I suspect your greatest challenge has been high temperatures.