Can't find a convenient test for this huge dataset :-(

Hi everyone,

I have some trouble choosing the right test for the following study:

I have a group of parents and a lot of ordinal measures. I want to test for each measure whether the parents resemble each other more on that measure than other random male-female pairs.
I already tried a permutation test (mix the parents up to make random pairs, which creates a null distribution), but that takes way too long to compute since I have about 300,000 variables/measures to test this on.

Any ideas?

Many thanks in advance!