"in your experience, how much heating? Enough to be problematic in a hot AND humid climate?"
Stick your hand behind the condenser outflow of a regular air conditioner. That will give you some idea. More heating BTU than cooling evaporator influence.
In the tropics, when air conditioning cannot reduce R/H to <50% we use a dehumidifier. This means an oversize air conditioner is necessary if the original power of the original A/C is borderline capacity.
The lower the ambient temperature the harder it is for a dehumidifier to extract moisture.