I see where you're coming from but I think the reason PTO doesn't compute ODC is that the dependent is not eligible for ODC unless an ITIN is issued on or before the due date.

According to Pub 972, the IRS does recognize ITIN issued after the due date so long as the application is submitted on or before the due date and one is issued as a result of the application.  If the W-7 is only submitted with the tax return, the dependent is still not eligible for ODC at the time of submission - until and unless the IRS subsequently issues one.

AFAIK, the IRS has not provided any clear guidelines for how such cases would be handled (unlike IR-2017-109, which clarifies that CTC would be restored automatically once an ITIN is renewed).  Your best bet might be to apply for an ITIN now, extend the return, and have your client settle any expected balance due by April 15.