The problem with joining ropes like that is you tend to be tensioning in a way that puts all of the stress at one point at the end of the loop. The way this is solved when you build kit planes is by using a steel thimble to distribute the stress around the loop, rather than at one spot.
You can do the same thing with a climbing carabiner. I would try tying something like a figure-8 loop on both ends and connecting them with the 'biner.
If you need the length to be variable, you can also pass an end through the 'biner, tension, and then tie a half-hitch with a loop. Then, tie another half-hitch around the cord with the loop.
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