Thanks for the advice; I looked into it last night. The problem ended up being the latch release rods, not the locking rods. I had never connected the inner lock rod, and the outer lock rod has a lot of play and is not threaded-adjustable anyway.
I ended up unclipping the rods from both the inner and outer releases, let everything go to their resting positions, then popping the threaded rods back in. Works great now!
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The lower/outer rod is now sitting significantly lower than before.