Gorgeous leather on your Alexa and it looks absolutely stunning on you. Thanks for posting such mega pics.
If anyone does want to loop the strap through to double it up - the size of the lobster clasp isn't really a barrier to doing this. You unbuckle the strap midway to take the short end and its clasp off. You can then thread the end without the clasp through the metal loop on the bag. You then buckle the strap back up again and clip both clips to the same loop.
I have done this as an experiment but never used the bag that way. I just punched extra holes like you did.