>... hornets have moved in in significant numbers. . . Does anyone have
experience with this problem?

I have had experience with that, unfortunately.  A weak hive of mine, late
in the summer several years ago, had hornets coming and going at will.
When I opened the hive up they would fly in from above.  They consumed
larvae, depriving the hive of its' next generations.  I wasn't ready to
give up on this hive, and didn't want to combine it with another for other
reasons.  I reduced the entrance, added a robber screen, added plenty of
pollen supplement and several gallons of syrup all to strengthen them.
Then, though not exactly standard practice, I donned a pair of gloves and
sat outside the hive entrance.  Any hornet attempting to land to get in was
slowed by the robber screen, at which point I, with those gloves, killed
them.  In total I got approximately 18-20 hornets in about an hour.

In the end it worked.  By the end of October they were back to having
enough stores for winter, and was one of my best hives the next summer.  So
there is hope.

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