This (2015) review reports that:

individuals are more likely to exhibit consistency when they focus abstractly on the connection between their initial behavior and their values, whereas they are more likely to exhibit licensing when they think concretely about what they have accomplished with their initial behavior—as long as the second behavior does not blatantly threaten a cherished identity

So broadly speaking I would expect the act(s) in question making public (or just making privately salient to you) a particular moral identity (as a person who acts well) would increase moral consistency effects, whereas acts which emphasis the amount of good you have done would increase licensing effects.