I'd start by adjusting the humidifier on the furnace. It sounds like you don't have to add any additional humidity to the air, so you could probably turn it down (or possibly off).
If you have a gas fired furnace, turning the heat up a bit could help. If the furnace does not have an air intake connected to the outside, the air used for combustion will be drawn in from outside. During the winter, the cold outdoor air has very little moisture. When the cold dry air is drawn into the house, it will lower the humidity levels in the home. This is why loads of people have dry skin in the winter, and the reason humidifiers are installed in the first place.
If none of that helps, you might have to consider installing a dehumidifier, or some other form of HVAC system to remove the excess moisture.
This is going to be sort of a comment, or at least not a complete answer.
When designing the system, the goal is not to create a breeze through the space. The goal is to control pressure equalization in such a way that the air is mixed and dehumidified (conditioned).
Having one large return at one end of the space, and a large return at the other may work. But it's not going to be as efficient, and will require maintaining an open area for which the air to flow (no closed doors).
Let's back up a bit, and think about how the system works...
The fan (or blower) is going to create a high pressure area "in front" of it, which causes the pressure in the supply ducts to increase. The higher pressure air flows from the supply ducts, in an attempt to equalize the pressure between the supply ducts and the rooms. At the same time, the fan (blower) has also created a low pressure zone "behind" it. The higher pressure air in the rooms is forced into the return ducts, in an effort to equalize the pressure between the rooms and the return ducts.
So the system works by forcing conditioned air into the rooms, and having unconditioned air pushed into the system.
Wherever you have a supply duct, you want to have and unobstructed return duct. Otherwise you'll end up with a high pressure area in one place, and a low pressure area in another.
In your example, if you have a single supply duct feeding the kitchen, and a single return in the bedroom. What happens if the bedroom door is closed? In fact, the bedroom door in your drawing would have a tendency to be pushed closed, if you installed the system the way you've described. You'll be creating a high pressure zone in the kitchen and living room, and a low pressure area in the bedroom. Which means the door could be closed by the pressure differences.
You'll want to install a supply and return in each separate area. In your case that would mean installing a supply and return in the living room/kitchen, bedroom, and storage area.
Unfortunately, duct design is a bit of science, and a bit of art. Covering all the information you'd need to know, would be nearly impossible in this short answer format. In my opinion, duct design is not a job for an amateur. At the very least, you'll want a pro to assist in that aspect of the job.
I know I've rambled a bit, and I'm sure you don't want somebody to tell you not to do it yourself. But in my opinion, it's better to have it done right, then to have it done cheap. Aside from all that I've mentioned. It's impossible for somebody to design a duct system without knowing the equipment you're going to use, or the actual dimensions of the space. So there's no way anybody on this site could provide a duct design for you, with the information you've provided.
My advice... Get an HVAC contractor to design the system for you, then you can do the work of installing it yourself.
Best Answer
If your house is too humid, it's because too much moisture is entering it. To fix that, you need to find the source of the moisture and reduce or eliminate it.
There are lots of places the moisture could be coming from. Humid air might entering your house from your crawlspace or basement (especially if you get water pooling after heavy rains), leaks in your roof, or leaky pipes are all common causes.