Sorry to hear about the anthias. On the drip, I generally start out slow 2-3 drops a second and speed it up to a steady flow toward the end of the process. I feel like for some species a long drip is overkill and may do as much harm as good. From a scientific standpoint, you want the temp and pH to be the same. Once they are, the acclimation is done. 40 minutes doesn't sound like too long of a time to go.

This is not exactly by the book, but I brought some fish home the other night (from a system that has no copper), I floated them for 15 minutes. Then I cut the end of the bag open and allowed them to "self acclimate". They stayed in the bag for about 10 minutes, they gradually moved toward the opening, and then swam out on their own. I assume the way I did it, there was mostly bagged water at the end, and a mix zone in near the opening. Obviously this is only an option if you 100% know the water in the bag doesn't have copper or other chemicals. I felt like this was a low stress way of acclimating though. (Your mileage may vary depending on situation and species.)

I also agree that chasing the fish with a net in the bucket isn't ideal. I would do this in a darker room where they can't see quite as well. Also maybe have a second bucket and pour the water out so they are easier to catch...or poor it all into a big net and the fish will automatically be in the net. Also, I think adding fish to a dimly lit tank and leaving lights on low for the rest of the day is not a bad idea either.

Is there any chance you have something snacking on them in your tank?