Just a little update. I wrote to Waverly, (Stewart MacDonald), with my concerns regarding the conical taper. They said that they should be OK as long as they are not over tightened, (not really very comforting). I also wrote to Tim Laughlin, and he wrote back with a nice and detailed letter. Tim feels that the Gotohs are a better tuner, but likes the vintage look of the Waverlys. He did not dismiss my concern, but he said that he has never seen a split head caused by this type of tuner, or any taper tuner.
I like the nice vintage look of the Gotoh friction tuners, but I think that the Banjo size buttons that they use, (and Grover too), look too large for a Ukulele. I was able to buy some Ivoroid banjo buttons from Stewart Macdonald and machine them down to the size of a late 1920s Martin button. They look great on my Martin 3K with Nickel Gotoh tuners, but the screws are still Phillips, so making screws will be the next task. After that, I will change out the Waverly tuners on my Laughlins to Gotoh with modified buttons and custom screws. I consider the Laughlins to be irreplaceable, and I would hate to pick one up some day and find a crack in the head. It may be unlikely, but I don't think that the risk is worth it. My goal is not to hurt sales of Waverly tuners. I simply wanted to voice a concern, so please take it with a grain of salt.
I also asked Stewart MacDonald if they had any plans to make an accurate vintage type replacement tuner for ukuleles that was not the current Waverly. They told me that they would pass that suggestion along and that they were always looking for new products. If anyone in the UU community would like to see this happen, an email to Stewart Macdonald might be helpful. If they receive multiple requests, we might see a good, vintage style replacement that does not require custom machined parts or the risk of cracked heads.