CSS: Making a 'class' exempt from overflow:hidden

So I'm working with a CMS platform and am trying to implement some nifty CSS written by our very own JimSA.
Directly put: my desired class tag is housed inside 3 or more other Class tags which have overflow:hidden in them, so when the intended object appears (consuming the space of many classes and IDs) it gets obscured to the boundaries of it's class. I change the overflow to visible, which defaces the layout of the area, the intended object is obscured at the boundary of the next class in the hierarchy - which I have done before at the cost of aesthetics.

Live:
http://test.nagualgrove.com/img-test.html

So I'm wondering if I can do anything to let this class display freely on the page without having to change the neighbouring CSS.

Thanks for your time.