How can I deal with a heat pump condenser producing lots of water?
Heat Pumps are basically where you reverse the process of cooling in your HVAC. Normally your compressor takes the expanded hot refrigerant and runs it through the coils to cool it down, before sending it into the compressor, where it's compressed and piped into the blower, where it's allowed to expand (gasses cool as they expand) and become hot.

A heat pump reverses this process by sending the compressed refrigerant back through the coils. So your coils are expanding the gas and thus cooling the outside to bring heat inside. What you're seeing is the normal byproduct of this process: condensate. In many cases, this is actually a defrosting because the outside coils get pretty cold (and North Florida has been saturated with rain of late so humidity is quite high).

The only thing I could think of to control this would be to install a water heater pan underneath and pipe the condensate elsewhere. You'll need to probably build something else to hold the unit in place, since it's screwed to the pad.