You are going down the recommended path, so it sounds like you just need a couple tips of how to go about it.

The code you've found shows how you can modify a submission before it gets stored:

// Subscribe to form submitting event.
Submissions.Submitting += Form_Submitting;
private void Form_Submitting(FormSubmissionContext context)
{
    // Modifications here.
}

You can subscribe to the event from an ApplicationStarting event: https://our.umbraco.org/documentation/reference/events/application-startup

Inside of that, you can modify the values of the form submission. If you make one of your fields a hidden field, you can modify its value. Note that you can't "add" a field dynamically, but so long as the field is already there to start with, you can change its value.

Here's some code that's doing something similar:

/// <summary>
/// Sets the success indicator field to "Unknown".
/// </summary>
/// <param name="context">
/// The form submission context.
/// </param>
private static void SetSuccessIndicatorField(FormSubmissionContext context)
{

    // Find the success indicator field (exit early if not found).
    var field = context.Form.Fields
        .FirstOrDefault(x => x.Category == "Success Indicator");
    if (field == null)
    {
        return;
    }

    // Get or create the field data.
    var newData = new List<FieldSubmission>(context.Data);
    var fieldData = newData.FirstOrDefault(x => x.FieldId == field.Id);
    if (fieldData == null)
    {
        fieldData = new FieldSubmission()
        {
            FieldId = field.Id
        };
        newData.Add(fieldData);
        context.Data = newData;

    }

    // Set field value to "Unknown".
    fieldData.FieldValues = new List<string>() { "Unknown" };

}

You should be able to adapt that for your purposes.

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