We've got the same with crows. The best solution so far was to string fishing line across the top of the run. They can't really see it so some hit it and get tangled. Then the others stay off. They've all been unhurt and I've released them so not 100% humane but not awful either. It might be less successful with starlings because they're smaller birds (and probably not quite so clever as crows so they might not look at one tangled bird and associate it with danger) but it's low cost and worth a try!
You can also buy rope bangers- it's what the farmers use to keep crows off their crops. They go off every half hour for about six hours. We found with getting somebody to shoot them, they just flew off while the shots were going on and stayed away until they stopped. So this is an easier way of getting regular shots without somebody needing to lie there with a gun!
H