To start with, if their rules regarding random testing allow them a given number of tests, you have to argument for that many random tests. I haven’t seen any entity actually limiting their rights to test to some given number of tests though. Unless it actually limits the number of tests rather than suggesting you should expect 1-2 tests per year, ya got nothing unless you can show the testing appears to be punitive in some way.
It sounds like yours are not part of the random testing though. It appears the tests are for cause. You need to understand the policy for what is considered to be for cause and deal with that.

