Just an amateurs POV but offered as someone who was recently off work for some time: don't "we" tend to have to be fit in some areas of our health to a higher standard than the general public and therefore there are plenty of conditions which might not raise much of an eyebrow with the GP/local health authority, quite probably conditions they won't test for, and won't fund testing for, but which might cause justifiable concerns to an AME/the aviation regulator.
Our national regulators website has lots of info on disqualifying conditions and test required, does yours do similar?
As to the recommendations.I assume despite your AME's thoughts on who to go to you are actually free to "source" the tests elsewhere?