question

You could write the parameters to an excel file in the On Start Of Replication trigger of the experimenter.

The code below assumes that all parameters are numerical values. I do not know the format of how other parameter types would be stored in the task map, since this is, as far as I could find, not documented anywhere. The code is based on some trial and error experimentation to find out where and how the paramters are accessible in the trigger. (And you would of course have to adjust the file directory and sheet name.)

Object current = ownerobject(c);
int replication = param(1);
int scenario = param(2);
Map task = param(3);

excelopen("D:/ScenarioParamsTest.xlsx");
excelsetsheet("Tabelle1");

// Find next empty column
int col = 2;
double cellValue = excelreadnum(1, col);
while(cellValue != 0)
{
    col += 2;
    cellValue = excelreadnum(1, col);
}

// Write data to excel file
excelwritestr(1, col-1, "Scenario");
excelwritenum(1, col, scenario);
excelwritestr(2, col-1, "Replication");
excelwritenum(2, col, replication);

Map params = task["parameters"];
Array names = params.keys;
for(int i = 1; i <= names.length; i++)
{
    excelwritestr(i+2, col-1, names[i]);
    excelwritenum(i+2, col, params[names[i]]);
}

excelclose(1);