Everything is driven by data - so yes, you need to request testing. I would also request a FBA that can lead to a BIP that includes more than just "work completion." Data (present levels) then determines goals. You can't change goals until you know what the data is, and it doesn't sound like you have good data.
Chances are you will not like the results of the school evaluation (will likely not have any suggestions for how to address EF), so be prepared to request another IEE. Make sure both the school eval and IEE are for ALL areas of concern, including transition. A good IEE regarding transition should show what EF skills are missing and what should be taught. A good IEE/FBA will also show that head down behavior is not a choice, is related to his dysregulation, and is something that needs to be addressed with goals and in the BIP. In order to "communicate this to the team" and make them "see it," you need data.
You will not be able to accomplish this prior to the annual meeting, but IEP's can be amended at anytime and IEP meetings should be held after additional data is received (in the form of the school's eval and later the IEE).