How to remove moisture from cheese that is stored in a liquid?
The tool for the job is a cheese press, though for small quantities a tofu press (I have one similar to this) works well. I bought mine for home-made paneer and bought tofu, but have also used it for halloumi and mozarella (home made, not brilliantly successful).

The idea is simple: wrap the cheese in a cheesecloth, place in the press, weight, and wait.  If your cheese doesn't have flat parallel sides the design I've linked above won't work as well; there are more piston-like shapes that keep the top plate of the press horizontal.

You can improvise with two plates, but it's fiddly, and the bottom plate should really have drainage holes.