Fully recognizing that I'm earning my screenname with this one...
The slip on dampeners make too many assumptions...
Ultimately, you have to have a harmonics problem for them to even be any benefit at all, which isn't always the issue with less-than-superb accuracy.
Secondly, a dampener (in the truest sense) CANNOT cause a 'disharmonic' barrel to become harmonic. Ballast can do that, but that's not what you're buying in the dampeners (ballast changes the vibrational frequency and/or node locations of the barrel). Dampeners will only reduce the magnitude of the disharmonics. Personal expectation: the ballast contribution supercedes that of the dampening provided by limbsavers.
Strapping ballast (essentially the dampener = dead weight) to the wrong part of a barrel can actually DECREASE accuracy by providing an additional vibrational node, and/or focal load.
Is the amount of dampening or ballast load provided by the fixed size of the limbsaver appropriate for the magnitude of disharmonics? Millions of barrels out there, but only one limbsaver design? Too much or too little = ineffective, or inefficient at best.
Positional testing is critical. You might shoot out your barrel just testing where that dampener should be positioned.
Should you have 2 dampeners/ballast? 3?
To me, it's much like the statement "inflate your tires to 45psi they'll go and they'll be more efficient." Which is very likely a correct solution for passenger cars. Then you take that to a guy that rides motocross and suddenly his front tire doesn't grip worth a dang and he can't keep his bike on the track because his tire is too hard. Or you take it to an 18wheeler that suddenly has 18 flats because his tires were too soft.
It's cheap, so if it helps at all, you're not out much, but for my money, I'm not interested in a one-size-fits-all solution that doesn't really have a good foundation to stand on.