Every time I've seen an Access Denied error while trying to invoke the Audit Trail report export script, it's been due to the ExportFile directory.

Read the instructions for that parameter closely. I've reproduced them here for reference:

  .PARAMETER ExportFile
  Target file, on the machine where Audit Trail is installed, to save the report. If the file already exists, it will be deleted first, then the new file will be saved with the same name.
  Supported file types are '.xlsx' (Excel) and '.csv' (TAB DELIMITED csv, not comma delimited). 
  If no file type is specified, e.g., "savedReport", '.xlsx' is used by default, unless the export has over 100k rows, in which case '.csv' is automatically used due to technical limitations generating large xlsx files.
  Explicitly using '.csv' is recommended for most use cases. E.g., "savedReport.csv". 

  By default, the export file is saved under '%ProgramData%\Laserfiche\AuditAnalytics\Export' on the server hosting Audit Trail Reporting. To change the export directory:
  1. Update the Audit Trail web.config file as detailed below
  2. Grant the "IIS AppPool\AuditTrailAppPool" local user access rights to the new export location.
  
  The export file is saved under the directory specified in the '<add key="ExportFolder" value="" />' setting in the '<appSettings>' section of the '.\Program Files\Laserfiche\Audit Trail\WebAuditReport\web.config' file. If no ExportFolder value is specified, the default ExportFolder directory is '%ProgramData%\Laserfiche\AuditAnalytics\Export'.
  If you want a different directory, please update the '<add key="ExportFolder" value="" />' setting in this 'web.config' file. It is a good practice to create a backup copy of the web.config file before making any changes.

  UNC paths to other servers or file shares are not supported. If you need the export file to end up at a remote location, either write a secondary script or make a copy of this script and extend it to copy/move the export file to the desired location once the export is complete (you can use the "ReturnValue" outputs to check for completion).

  This parameter takes a full path, e.g., "C:\AuditReportExports\savedReport.csv", which must be under the "ExportFolder" (including subdirectories). Audit Trail will attempt to create a specified subdirectory if it does not exist. For example, with the default ExportFolder (no value set in the web.config), this parameter value will create a subfolder named "2024-06-20" and save the export file as "savedReport.csv" within it:
  -ExportFile 'C:\ProgramData\Laserfiche\AuditAnalytics\Export\2024-06-20\savedReport.csv'

  If you specify a path that is not under the ExportFolder, you will receive an error message in PowerShell like:
  "'C:\\AuditReportExports\\savedReport.csv' is not a valid exporting path, please using a path
  under 'C:\\ProgramData\\Laserfiche\\AuditAnalytics\\Export', and the permission settings are correct. If you want another directory to export, please contact Administrator to change the settings of Audit Trail web site.

Assuming you have not modified the ExportFolder value in the \WebAuditReport\web.config file, start by trying with -ExportFile 'C:\ProgramData\Laserfiche\AuditAnalytics\Export\savedReport.csv'.