It seems to me that there are two problem areas here. Those related to play issues, cheating basically and those related to shouts.
99% of regular fibsters don't drop, dump or abuse multiple nicks. I can't speak for phone users, but most of us would happily lose them anyway. It's a great pity that Patti has to spend any time at all dealing with this, but while Fibs is a free server, there will always be a bit of it. Share the load Patti. I am sure that one or two reputable regulars would be happy to help with a bit of admin. I would, as long as it doesn't require programming skills.
I would estimate that less than 1% of fibsters ever shout at all and and of those the very great majority are not offenders, but shouts is still a problem area for Patti. I see three solutions. The first is to ban a few more problem shouters. The removal of those that we have already lost has immensely improved shouts and discouraged the worst abuse from those who remain. The second is to shut down shouts altogether. I expect that tourneybot can be adapted to message or tell everybody for tourneys or even be the only allowed user. I would willingly give up the pleasure that I get from using shouts to retain fibs.
The third is to allow a bit of load sharing. There are plenty of fibsters with good judgment who never abuse shouts, so use two or three of them to operate monitor, warning and then removing those out of order.
It's great that you provide Fibs Patti and if you pull the plug one day, who could blame you? Perhaps if you get in a little help around the place it will seem less of a chore and more of a pleasure.