This is a very big conflict between the compliance department, adverse action department and loan officers.
First, I am not surprised that you are having a conflict on which denial reason to use because the rules don't clearly tell us which reason to use - all they say is that you must provide a specific reason.
A bit of background on this; as far as I have been able to tell, the two reasons of excessive obligations and insufficient income come from the sample notification form C-1 found in Appendix C (which is optional to use). As this model form provides two DTI reasons for denial, many have believed that these reason are, in fact, separate and distinct and the general consensus on when to use these reasons seems to go back to a resource found on BOL called the Adverse Reason Chart (found here:
https://www.bankersonline.com/sites/default/files/tools/adversereasonschart.pdf.) This chart defines insufficient income and excessive obligations the way you have defined them.
Over the years as a consultant and speaker, I have taken the best practice approach that each denial reason on the AA Notice should be clearly traceable to the loan file. Therefore, I've typically recommended internal procedures (such as the referenced chart) to provide guidance as to when each DTI reason should be used.
For example, if an AA Notice lists insufficient income (and assuming the bank defines it the way you did), then I would expect the DTI in file to include the proposed payment and also be higher than your policy maximum DTI. Alternatively, I would bexpect that a reason of excessive obligations would include a DTI in the file that is too high but does not include the proposed payments in the DTI calcualtion. If both reasons were listed, I would want to see evidence in the file that the DTI was 1) too high before the proposed payment as well as 2) being too high after the proposed payment was added in - meaning that it would be ideal to have two DTIs in the file.
From my experience, every bank calculates the DTI ratio in a slightly different way as I have seen some banks utilize an underwriting template that calculates the DTI both before and after the proposed payment is added in. Other banks just run the DTI with the proposed payments while other banks may not even include the proposed payment if the initial DTI is too high.
For me, the bottom line is to make sure that your underwriting process aligns with how you list your adverse action reasons. How can you do this? First, you would need to determine how you calculate your DTI (whether you calculate it before the proposed payment is added, after it is added, or both). Next, you would determine how this will apply to listing your AA reasons. For example, if you calculate both the before and after DTI, you would want to list both reasons when applicable.
All of this said, the rules don't define the difference between excessive obligations and insufficient income, so a different approach to this (such as the one Randy provided) could be acceptable. For training and logistical purposes, however, I have just found it best to drill down procedures so that each denial reason can clearly be traced to the application file as this will ensure consistency for both for staff as well as auditors/examiners.