I have a thought, but not sure if it will work. Take a look at this tutorial:
https://slinging.org/forum/YaBB.pl?num=1196026630. It's a woven split pouch from two strands of paracord (this is actually a fun sling to make just in general). And here's my though to get what you're looking for. In the tutorial, the end of the paracord is left long on each side to form the retention and release cords. But I don't see what you couldn't fold it over and run it through the pouch. You could run it along with one of the core pouch strands, effectively just doubling it, and then terminate it at the other end of the pouch. Then instead of a release/retention cord you'll have a loop.
The only concern I have with that is it'll be a single strand of paracord you'll be connecting your actual cords too. That's not the strongest thing if they're rubbing against each other. You could probably reinforce it some way though.
Here's a great closeup of the pouch one of the other guys did from this tutorial:
https://slinging.org/forum/YaBB.pl?num=1172017416/3645#3645.