2 D density plot interpretation and manipulating the data

My understanding is that this represents bivariate normal
approximation of the data which uses the kernel density function to
test for inclusion within a level set. (please correct me)

You can fit a bivariate normal distribution by computing five parameters.
Two means, two standard deviations (or two variances) and one
correlation (or covariance) coefficient.
The bivariate normal *has* elliptical contours.

A kernel density estimate is usually regarded as an estimate of an
unknown density function.
Often they use a normal (or Gaussian) kernel, but I wouldn't describe
them as normal approximations.
In general, bivariate kernel density estimates do *not* have
elliptical contours.
But in saying that, if the data is close to normality, then contours
will be close to elliptical.

Kernel density estimates do not test for inclusion, as such.
(But technically, there are some exceptions to that).

I'm not sure what you're trying to achieve here.