Here's a video of me taking on something similar:
https://www.youtube.com/watch?v=SXSahXBQbbMThis is by far the roughest battle I've gone into, no major losses (only 1 jesuit) however two of my three karkinos were that close to becoming space junk. In my opinion, paragons do have amazing defensive capabilities and would be a great choice vs templar however I do prefer having overwhelming firepower and the ability to use templar kinetics. That being said, I think the karkinos is essentially a buffed onslaught: better manuverability, better armor, better focus fire (though less weapons) and better flux stats.
I also like having a bunch of random sacrificial fighters just to gain map control and be annoying. I was expecting a single priwin burst to take them all out but seems like that rarely happens.
My biggest mistake is being too aggressive in this battle, especially trying to camp their spawn (see 6:29). Most templar captains do tend to valiantly rush their ships into deathtraps and it would've gone better if I kited more.
As you can see by the end of the video, I think I've ran into a bigger problem.