Sweettea, my apologies for heaping on and assuming the worst after your continued line of questioning. I, and I'm sure others here, are certainly thankful to hear that you are moving forward and treating the problem properly.
Regarding the dehumidifier angle against energy efficiency: From an artificial, mechanical engineering standpoint, it roughly takes just as much energy to condense water out of the air as it does to evaporate it. This is why dehumidifiers are such an energy suck to begin with, and why drought stricken areas such as California are turning to recycling waste water and desalination - as expensive as these methods are, it's still cheaper than industrial-scale water condensers. Dehumidifiers are no more complex or amazing than air conditioners, and in fact work the
exact same way. The only difference is that you have both ends of the device indoors with the waste heat re-warming the air cooled over the coils to extract the water before being pumped back into the air - same guts but with none of the advantages of beneficial heat exchange.
The reason why heating the air is so much more efficient (mostly time-wise) than dehumidifying for drying is because heat not only accelerates evaporation, it permits the air to hold more water. Unfortunately, that removed moisture eventually has to go
somewhere - and that somewhere is out into the world. There's a reason why people in the past didn't really wash their clothes in the Winter. A lot of these technical limitations is the reason why - the RH, the temperature, the ease of drying, etc. Dryers are a miraculous thing for allowing clean clothes during winter months. Could they be more efficient? Certainly! They're a pretty inefficient machine overall, but there are ways to gain and game that efficiency.
The real places where the greatest gains could be had to increase efficiency of a gas or electric clothes dryer when needed is the application of a counterflow heat exchanger between the exhaust air and a dedicated air intake for the dryer itself (something that houses really aren't set up to do), in addition to a high speed spin dryer to remove as much liquid water as possible through centrifugal force before evaporating the rest.
May this additional information help you to better tackle the efficiency issue going forward after resolving the health issue.
Edit: I'm adding a link
to a few other alternative clothes drying methods. Some have utilized
dehumidifiers in connection with dedicated wardrobes/rooms for drying, which may be in line with some of your earlier thoughts. Ultimately though with the power poured in, even if a dehumidifier and fan has the potential to be more efficient overall with the longer dry time, the system is still pretty well closed with minimal benefit to the rest of the house.