Replace text in a Google Sheet and maintaining formulas

I have a Google Sheet that I would like to use as a template. A user submits a Form and a OnFormSubmit trigger makes a copy of the template and replaces certain text with the answers. I would like to use this in several applications and the locations of these text fields may change, so I would rather not specify a specific range or Named range for every replacement.

Using some tidy code from this question I can do exactly what I want. Except, formulas that I have in the template are removed using this method. In other words, a cell in the template has =E10*F10 but after the replacement the value is either blank or 0.

Is it possible to fix this within the code that I have? I can't find a solution except to try a different approach perhaps...

function replacetext(target,key,value){
var spread_sheet = SpreadsheetApp.open(target)
var sheet = spread_sheet.getSheetByName('Sewage Flows');
replaceInSheet(sheet,key,value);
}


function replaceInSheet(sheet, to_replace, replace_with) {
  //get the current data range values as an array
  var values = sheet.getDataRange().getValues();
  Logger.log("values: " + values)

  //loop over the rows in the array
  for(var row in values){

    //use Array.map to execute a replace call on each of the cells in the        row.
    var replaced_values = values[row].map(function(original_value){
      return original_value.toString().replace(to_replace,replace_with);
    });

    //replace the original row values with the replaced values
    values[row] = replaced_values;
  }

  //write the updated values to the sheet
  sheet.getDataRange().setValues(values);
}