"disam page for that makes extensive use of the NFL abbreviation that is not used in the title of the main article.  So I think we've got precedence to use ISIL in a disam page, if we choose to.    
 Re the ""US-centric"" ISIL (which is also commonly used by a large number of governments and several other sources). we could equally use another reference to the ad-Dawlah al-Islāmiyah fīl-ʿIrāq wash-Shām title such as Daesh or ISIS.  The "