If you pull air from the basement, it's going to get replaced with warmer, wetter air from upstairs. As it cools the air is going to deposit that water on the coolest surfaces. You might be trading this problem for another, more damaging one.
Good point, I'll have to keep that in mind. I would think that after the initial temperature equalization, it shouldn't be an issue as long as the temp remains relatively stable afterward, so in theory, if the rate of the initial equalization is gradual enough, I would think it wouldn't cause any long-term issues.
Though that does depend on how exactly any possible solutions would work, and how controlled they could be. I might just re-evaluate after I get the insulation work done.
I live in a geodesic dome and the finished basement is always noticeably cooler than the main floor and top floor.
As a test, I got a blower fan and put it at the basement stairs blowing the air from the very bottom of the house up towards the middle floor.
After about a day the temperatures equalized enough that it was difficult to tell the difference between the Middle floor and the basement.
Doing that causes the colder air to mix in with the warmer air upstairs, and the registers pull the warmer air in and blow out dehumidified air back into the basement, so no moisture build up.
The only downside is the noise and energy costs to run a fan. Probably 400 watts.
What I want to do is get a 4 inch duct fan and place that in the wall and run ducting from the basement up to the top floor so that the cold air is constantly being reblendid back up with the rest of the air upstairs.
I feel like that would use much less power and do a decent job of blending the two.
Maybe you can find something like that that will work for you.