The reason sealed containers don't seem to work is because you still have to open them. When you open, you let in air with moisture. When the container cools below dew point, that moisture condenses and much of that condensation is absorbed (with a "b") by the toilet paper. If that was the end of the story, there wouldn't be much problem. The problem is when you repeat the process. You open the container, let in moist air, cool, and so on. This creates a sort of "ratche" effect because water is absorbed by the TP fibers but never allowed to evaporate efficiently.
In fact, if you frequently open it, the container is actually worse than just leaving the TP out in the open. At least, out in the open, its dampness is pretty limited, provided you reasonably manage the temperature and humidity in your cabin. That is, you have less "ratchet" effect.
There are four ways around this cycle.
First, just leave it out and control the temperature and humidity of your boat. The key to this is to truly leave it out in an area of good circulation. Depending how RH and dew point corelate in your environment, this could be completely fine. Around here, that's a good enough strategy. However, if interior of your boat routinely alternates to temperature above and below dew point, then you will still get that moisture "ratcheting" effect. Water will condense, be absorbed away from the surface of the roll (where it would have been allowed to freely evaporate), then the cycle is repeated.
Second, put it in any airtight container and never open it. That sounds like a joke, but really I just mean that you break your TP into smaller portions and put those in sealed containers (probably bags). The moisture in then individual packages will not increase as long as you don't open them. So, the idea is that, once you open one, you will use the ingredients in a day or two.
Third, decrease the amount of air in the sealed container, relative to the amount of TP. This is why bags seem to work better - because there is less air space surrounding the TP. The amount of moisture that can make it to the TP is directly proportionate to the volume of air surrounding it. Decrease that volume and decrease the problem. Vacuum packing would just about eliminate it entirely, but that's overkill. Just squeezing out as much air as you can before sealing the bag should suffice.
Fourth, and probably the best: Give the water molecules something more attractive to do. That is, add a desiccant, such as silica gel packets that come with certain foods/medicines. A desiccant will adsorb (not absorb) much of the water before it gets a chance to condense and be absorbed (with a "b") by the TP. The mistake most people make, though, when using a desiccant is they put it low in the space they are trying to keep dry. Better to tape it to the lid of your TP Tupperware. The reason is that this is where the inside of the container cools most rapidly and where condensation will tend to occur first. You want to keep that air as dry as possible.
Or, just take to open-water swimming and forego toilet paper altogether.
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