Well, there's

INGRATIATE

E ==> O

GRATIATION

No, I never heard of the word either, except maybe as the opposite of ingratiation. And there's no listing in OneLook.com either. But there are 2,200ish hits on Google.com, and in particular one might look at Table 2.5 here [drop down four or five screens worth and you'll find it], talking of the "gratiation effect of the Moon since its formation 4.45 billion years ago (bya)" making the Earth's day slowly longer. Hard to judge the validity of the site, though.

Personally I'd just as soon go on from INSTIGATE, but however the consensus would like to proceed is OK with me. (For that matter I'd even go with the capitalized words to broaden our scope, but I'll stay within whatever limits we collectively decide to adopt!) ;-)