I don't want Squeak to get Diseased, because I like the idea of fielding a team without Diseased if I choose. That said, I've never put influence on Squeak. I've never thought it beneficial, which is too bad, because Dreadful Shriek is cool, but with Tac 2, you absolutely need a charge to hit anyone with armor. 2 influence is a whole Rataclysm, I'm not paying that to maybe get Dreadful Shriek off. Predatory instinct helps somewhat, but not enough for me to commit influence to him. At this point he is a slow, opportunistic crowd out, that I hope doesn't become a momentum farm.
I haven't really tried Bonesaw or Graves in Ratcatchers yet, but that's because the main lineup is so good. Bonesaw seems superfluous in a team that must take Piper, and has access to 3 die kicks in Miasma and Pelage, who also have a serious beat down capability and passive effects on top of their footballing. Bonesaw is super capable of janky goal runs, but the in built jank of the Ratcatchers makes him unnecessary, and the other players are contributing to more than just goal runs.
Graves is a little different. I see him teaming up with Scourge in a scrum in a great way, and not just because of Snackdigger/Gravebreaker. While Scourge has knockdowns, the one on 3rd is non momentous, and I'd much rather do his momentous 2(+1) on 2nd. With Graves, you can get reasonable knockdowns (plus Gravedigger/Bleed), and then use Scourge's attacks to get juicy, momentous, high damage results. The only problem is who to drop. Miasma helps your Diseased game, has Salve, 2" melee, Rataclysm and Erupting Spores. Pelage has so much passive damage you don't even need to give her influence (although you should, because she gets work done). Skulk is the best goalie/striker cover in the game, and can shut down a football team basically by himself. I don't see the situation where I'd rather not have one of these models just to tee up Scourge with knockdowns. And I certainly wouldn't want to replace Scourge. People generally value vGraves for his knockdowns, but Scourge has it on the same column with 2 more Tac, and does unholy amounts of damage. I need a better reason for taking Graves than boosting the mascot that I already give no influence to.