I repair mandolins and never have a problem with them. I have a friend that has asked me to research and install a mandolin pickup but quite honestly, I do not have a clue as to the 'inside' on a good mandolin pickup. I've repaired mandolins with pickup systems that sound great but I'm not up to speed with the blue grass circle enough to determine a good choice. I've asked a few grass players, but none seem to lead me to a one or two choice consensus. My friend didn't seem too hot on the idea of a saddle type pickup so that kind of narrows things down to a contact type pickup. The mandolin in question is a Webber Gallatin which I'm sure will help with any opinions. I suppose I could spend a few days at Merle Fest but its a ways off and I like to see if anyone here has expertice in the area of mandolin pickups...
I agree on the Fishman--by having to replace the saddle, you're stuck with inferior material and it won't sound as good unplugged as a good Loar repro, like a Cumberland Acoustic. And it has that unmistakable piezo quack.
I have to disagree about under the top pickups, at least with reference to the K&K. It sounds nearly as good as with a mic, doesn't feed back appreciably (I've used it with condenser mic and SM-57/58 setups) and doesn't change the unplugged sound. No hollow sound, either. I play Bluegrass and the K&K sounds just fine for that. It has enough output that I can go directly to the board without a DI if need be and the EQ on the board is adequate to get a good sound.
I had a Baggs radius and it was very shrill and created a lot of feedback. Maybe that was because I put it on a bandolim, which is brighter than a carved top mando, but I took it off and sold it after a few tries because it had too many problems and didn't sound anywhere near natural, even through a Baggs Para acoustic DI.
Good non-piezzo contact microphone can be found in Schertler's catalog. Very good products. I advice these on instruments played in a quite quiet configuration (acoustical music mostly).
My issue with K and K is servicing them. If they are installed the recommended way, they can't be removed with out damaging them and leaving pieces of glue and brass and ceramic stuck to the bridge plate. This makes it difficult to replace them. I have had 4 come in to my shop in recent years with one side not working. They sound pretty good but I'm not a fan.
While Ron Ellison may not know mandolin bridges. He has a good knowledge on how piezo pickups work and has provided us with a close approximation of how K&K pickups are manufactured.
I have installed the LR Baggs Radius Transducer Pickup. It works great, does need a preamp, but with a modeling pickup you can get exactly the Bluegrass sound you want without altering the mandolin in any way.
I meant model in preamp provides the sound you want