New house - No neutral in switch box?
3-way switching, switch loops, 404.2(C), and you

NEC 404.2(C) is where the requirement for neutrals at switch boxes lives (quoted from the 2014 NEC):


  (C) Switches Controlling Lighting Loads. The grounded
  circuit conductor for the controlled lighting circuit shall be
  provided at the location where switches control lighting
  loads that are supplied by a grounded general-purpose
  branch circuit for other than the following:
  
  (1) Where conductors enter the box enclosing the switch
  through a raceway, provided that the raceway is large
  enough for all contained conductors, including a
  grounded conductor
  
  (2) Where the box enclosing the switch is accessible for
  the installation of an additional or replacement cable
  without removing finish materials
  
  (3) Where snap switches with integral enclosures comply
  with 300.15(E)
  
  (4) Where a switch does not serve a habitable room or
  bathroom
  
  (5) Where multiple switch locations control the same lighting load such that the entire floor area of the room or
  space is visible from the single or combined switch
  locations
  
  (6) Where lighting in the area is controlled by automatic
  means
  
  (7) Where a switch controls a receptacle load
  
  Informational Note: The provision for a (future) grounded
  conductor is to complete a circuit path for electronic lighting control devices.


In particular, point 5 above is what applies to your situation.  Unfortunately, the normative text of that section wasn't a model of clarity, and this section was reworked in 2017 to try to fix that.

So, you'll need to talk to your electrical inspector.  My interpretation of the 2014 text is that you need a neutral at at least one location in a multi-way switching system, but not at every location in said multi-way switching system -- there is room for reasonable people to disagree here though.