followed by giving them a frame of brood from another hive.
That is the bit that I noticed. Not sealed brood, I hope. Or you may be introducing as many mites when this hatches as was on the swarm!
The 20% (or 15%, if you subscribe to a more precise figure) on the bees is a bit of an assumption also. Assuming half the bees went with the swarm is halving the number of mites with the swarm and that is assuming the varroah are evenly distributed throughout the worker bees, which they are not (varroah will not necessarily especially choose not to cling to a non-flying house bee, just because the colony is about to swarm).
So Victor is right, there will be relatively few mites with a swarm (always relative, of course).
There are better ways to treat (virtually as effectively) as oxalic acid without the possible down-sides of oxalic acid treatment (on the queen mainly, as the rest of the bees will be dead within a couple of months).
For instance, removing the first capped brood from the swarm will trap most of the mites without any risk of using potentially damaging chemicals. KISS principle in operation here?
Regards, RAB