I am working on this problem too, and am also having issues.
So if we use the WKB approximation, we really just need to find p(x) and p(xo), which will be
$$p(x) = \sqrt{2m} (E-U(x - \frac{L(t)}{2})-U(x+\frac{L(t)}{2}))^{1/2}$$
right? I'm not sure what else to do with it though.