Right now I need to keep windows open throughout the year which causes quite a bit of extra heating costs.
If your need is for heating, not cooling, at the same time as lowering humidity, then why not use a dehumidifier?
I've been using small portable units for several decades. For a long time I was using De'Longhi, but both units I had finally died (after maybe 20 years of 24/7 use from mid April to mid November!) and I now have a Panasonic F-YCL27N which is actually quite a bit more efficient. Both the De'Longhi and the Panasonic put out about 900W of heat, the old De'Longhi used 330W of electricity to do that, the new Panasonic 280W (measured). It's the start of winter still, I was away all of April and May and there was summer before that so the house walls and furniture has quite a high water content. So it's currently (after exactly 1 month of use) outputting about 12-15 liters of water a day. That will decrease by maybe half as the house and contents equalise to the ~50%-55% I keep the air at (it's usually 70% to 90% outside). That takes about 3 months of 24/7 operation.
The input power -> output heat ratio is not as good as a heat pump with indoors and outdoors heat exchangers (they push 4:1) but it's still pretty good. That unit currently costs NZ$732 (US$445).