Picking up swarmed hives with a portal gun deletes any custom data they had, making them not drop anything when re-placed.
The best method for automating swarmed princess production would indeed be quarries, however. Horizontally, Swarmer hives can generate about 20 blocks away from the alveary (~40 from edge to edge). Vertical range is one block below, 40 blocks up.
Create a floating alveary with all 21 possible exposed blocks converted to swarmers (the entire bottom layer, the perimeter of the middle layer, and the four corners do the top layer. Place a ~80 by ~80 warded block layer right above the alveary and put a (few) quarry(s) above that. Leave the quarries on with a small amount of juice and they'll collect any Swarmer hives that form.
Power your farm with a few alvearies producing aromatic drops and royal jelly for aromatic lumps, and swarm away.
Note that hives may form right next to the alveary or under the platform. This can be mitigated by filling the area below the warded blocks down to one level below the alveary.
Swarmer hives can only spawn next to other blocks, but I'm not sure if the game decides to spawn a hive and then checks for a place to put it, or if it finds a place to put it and then has a chance to spawn. If it's the latter, putting pillars of warded blocks in your spawning chamber to act as growth platforms will greatly increase available surface area, and in turn, productivity.
I will toss a farm together to test that.
Edit: Who knew that neither the filler nor the wand of equal trade work with warded blocks? Not me.
Swarmer hive stuff.
Edit 2: UGH! I built a prototype farm that would automatically grow swarmer hives in a quarry area that was being kept active by cobblestone generators (so that the quarry would not "finish" and turn off) and it was working perfectly! A buried alveary in a closed loop maxed out with swarmers was being fed aromatic lumps via pneumatic tubes, a transposer, a diamond chest, and an item tesseract.
Hives were being generated in the quarry pit and I thought I had just automated princess production; until I realized that swarmer hives broken by the quarry would not yield princesses!