What advantage(s) are there for the HondaJet's engine mount position?
Probably the reasons are similiar to the reasons which lead to the same mounting on the VFW-Fokker 614.


  This arrangement was used to avoid the structural weight penalties of rear mounted engines and the potential ingestion problems of engines mounted under the wings. This allowed a short and sturdy undercarriage, specially suited for operations from poorly prepared runways.


// Update  

The space in the cabin should be the actual reason in this case.


  “I had the idea around 1996,” says Fujino. “The cost of a business jet is very high. To reduce the cost, you have to reduce the size of the aircraft, but then you sacrifice comfort. I wanted to make the aircraft smaller, but not sacrifice the cabin.” Most business jets have the engines mounted on the rear
  fuselage, and moving the structure and systems to support the engines out of the fuselage would maximise space inside the cabin without increasing the size of the aircraft, he believed.


As always, there are pro and cons:


  The problem with an overwing engine is
  that interference between the nacelle and
  wing can accelerate the airflow and cause
  a strong shockwave, reducing the drag
  rise Mach number – the airspeed at which
  shockwaves form and drag begins to rise
  rapidly. Fujino says computational analysis
  and windtunnel testing enabled Honda to
  find a “sweet spot”, an overwing engine
  location that minimises the shockwave.
  The result, he says, is a 5% better lift-to-
  drag ratio – aerodynamic efficiency – in the
  cruise than a rear-engined aircraft.