The logical choice I think here is that you send as soon as possible, so as to not delay your application processing. But you know, thats just me.

When updating your letter, make sure it does not deviate too much from the first....as in, dont change the format and language entirely. Dont forget to include an explanation letter as to the purpose of the additional reference letter and the changes within.
Alternatively, you could wait and keep ordering GCMS to see where you stand. If they put your file under additional review, you then send the revised letter. Completely up to you at this point. My suggestion is sooner rather than later!