He use of drones within other countries' borders is consistent with which school of thought?

It is consistent with neoconservatism. The aggressive approach to the use of hard power is the main objective of neocnservatism. The advantages of neoconservatism are that the US is less involved in international process and can move faster to suppress conflict. Examples of neoconservatism are the use of drones as counterterrorism weapons in Barack Obama's administration, the Iraq War in 2003, and the 1980's US campaigns in Central American countries.