Another option is to select the equipment size based on the cooling load and add a dehumidifier to the duct system.
We used our heat pump with a Honeywell Prestige thermostat for dehumidifying beyond the cooling set-point and it worked well, but it would take the temperature below the setting. Last summer we installed a dedicated dehumidifier that also works with the thermostat dehumidification controls. That eliminated the temperature overruns and used a much smaller compressor than the one in the heat pump to perform the task.