Awesome. I would consider that calling the dive beforehand. Excellent decision! You would get brownie points in my class and we would modify the plan as necessary to meet both requirements and expectations of the students. There isn't a requirement to dive to the maximum allowable depth for certification, although there might be that expectation from students. You could do most of AN/DP shallower than 100'. If your personal tolerances were to less than 130, it can be accomodated. But you are a bit of an outlier there. 10's of thousands of dives on air to 130 feet are conducted every year, very few people have debilitating results from that.
And I'm not a CCR instructor, but I'm pretty sure that Advanced Nitrox is a required part or pre req of any CCR class. It certainly was for my initial IANTD CCR course. Actually, I just checked the TDI standards, you only need TDI nitrox (ie not computer only nitrox) for the Air Dil CCR, but you would need both AN/DP for Air Dil deco CCR.
I think most of the people saying AN/DP should be taken first are considering the skills, not the depth, as being important. It's also nice to find out if you absolutely despise hovering in midwater for 20 or 30 minutes BEFORE you drop $15k on a CCR and associated training.