"Export Layers as Files" with the original file name as prefix

It sound like you need to add logic into the file name routine to make it like the Image Processor scripts.  They will not overwrite files.  If the output file exist the will add a suffix sequence number that is unique. the function in Image Processor script look like this. Copy export layer to file to a new script  name and see If you can add that type of code and use the modified script to do your  work.

///////////////////////////////////////////////////////////////////////////////

// Function: CreateUniqueFileName

// Usage: Given a folder, filename, and extension, come up with a unique file name

// using a numbering system

// Input: string for folder, fileName, and extension, extension contains the "."

// Return: string for the full path to the unique file

///////////////////////////////////////////////////////////////////////////////

function CreateUniqueFileName( inFolder, inFileName, inExtension ) {

   inFileName = inFileName.replace(/[:\/\\*\?\"\<\>\|]/g, "_");  // '/\:*?"<>|' -> '_'

   var uniqueFileName = inFolder + inFileName + inExtension;

   var fileNumber = 1;

   while ( File( uniqueFileName ).exists ) {

      uniqueFileName = inFolder + inFileName + "_" + fileNumber + inExtension;

      fileNumber++;

      }

   return uniqueFileName;

}