I really want to know how near-infrared absorption lines correlate with emission lines; understanding this is essential for near infrared calibration.

The emission lines correlate reasonably well, but not perfectly.  There are models out there of how these should behave, but they seem to be proprietary and non-free so I have no interest in them - I won't pay before I know they work, and I can't test them. But perhaps more careful measurements of the night sky lines could provide some information about the absorption, particularly in the Brackett-delta and Brackett-epsilon region we've been interested in lately. I'm pretty sure the change in slope observed above is from observing at different airmasses (2.3 vs 1.05)