For exact answers, think not of helicopters!
The basic causesfor helicopter cross couplings are complex, and the sum of several factors, some of which cancel each other to some extent.
Dumping collective makes the nose go down, mostly because of the horizontal tail angle change, somewhat because the CG might be aft enough to contribute, and somewhat because at the new collective position, the cyclic is now not at the trimmed position.
To slice out each, set up a small experiment for each. The tail has no effect in a hover, so set a high hover and lower the lever. If the nose dumps down, it was not horizontal tail angle change, so look to the other two factors.
Then do the hover experiment, but with a vastly different CG. Apply logic to the results.
My experience says horizontal tail is the biggest factor, but all are contributary.