Will the new Part 23 changes reduce the cost of avionics for existing aircraft?
Unfortunately not: the purpose of the part 23 rewrite is to make it easier to certify a new aircraft type (not individual avionics or other systems) and it doesn't apply to existing aircraft. AOPA has a good overview, including this (emphasis in the original):


  10. Are the performance-based standards applicable to all aircraft?
  
  No.  The new process of using performance-based standards is limited
  to new airplanes certified under Part 23, which would include
  airplanes with a maximum passenger-seating configuration of 19 or
  less, and a maximum certificated takeoff weight of 19,000 pounds or
  less.


To address the cost point directly, in theory if the part 23 rewrite creates additional demand for new aircraft, and if those aircraft use avionics that can also be retrofitted to existing aircraft, then the increased demand might reduce prices. But that's highly speculative.