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On the off-chance anyone comes across this, I never ended up figuring out the cause of this, but it is clear that the bridge on this piece causes some kind of deforming force to be exerted on surrounding elements. What I ended up doing is moving things around so that the tubes are level with the bridge, as shown in the attached image, and the whole thing could be printed upside-down without support. When I printed this, it actually still came out with problems, as the bridge had somehow caused both of the tubes to shrink -- both were about .25 mm smaller than they should be, which implies that the support on my previous part was not the cause of the problem. I got around this on yet another print by setting horizontal hole expansion to 0.125.