I was also under the same impression ( me and my wife belong to different caste but not different religion ). We got court marriage done before I moved to Canada. Then after 6 months , we got Indian traditional wedding.
We submitted application with only court marriage photos --> side note : do have enough people in your court marriage so that you can genuinely show that there were people in your marriage ( even if it was a simple court one )
I later got to know from a FB group that a girl who is in India and her husband is PR here got just court marriage done in Sept, they submitted app in Oct, got PR approved in December itself , while we're still waiting for PR.
SO EVERY CASE IS DIFFERENT. DO NOT GO ACCORDING TO GENERALIZED STATEMENTS ON FORUM OR FB.
I would say do not go for common law as for that you need minimum 1 yr co habitation, etc etc.. which will add to your documents list. Just my view.
give additional supporting documents like : chats, photos, social media proof and a very good letter stating your reason. Get that letter reviewed with 2-3 people you know and ask them : do you think from our letter that our marriage seems genuine ? untill all of those 2-3 people don't get completely satisfied, keep fine tuning the letter and add details / shorten it up accordingly.
hope this helps !