For a GUE tec pass, the limit is 3" up and down, but it is really a limit; 6" is a bit too much - imagine that the limit for a "rec-pass" is 5". About being horizontal, the limit for a tec-pass is 20°, do you believe you can maintain such a trim during exercises?
Now, keep in mind these two points:
1) there are reasons for these limits; especially in overhead environments, I believe they are important.
2) instructors teaching for different training may choose different limits.
Frankly speaking, I can see why a good instructor may want you to first do core skills training if you have a 6" depth variation during core exercises. In my opinion, go for advanced training now is a bit too much. But that is just me

It's up to you the decision to train much more your core skills or to go for advanced training.
P.S. it is important that you are sure about your skills level; if you believe that your depth variation is 6", but you do not test it - that value may result to be very far from reality (in a negative or in a positive way) [EDIT: obviously, an evaluation dive is the best way to assess your level

]