After being in ex-boyfriend/ex-girlfriend mode on how to change my profile picture for 24 hours , something pop into my mind.

Gluttony is habitual greed or excess in eating, it must stay hungry and keep eating. We focus too much in letting it get move set of it's victim, but seldom discuss on how to give it a reason to keep eating endlessly.

Fire elemental is an existing pieces that have a reason to keep attacking, i am thinking that Gluttony should get cost decay by time so that it need to keep consuming other units.
As to balance it's power, Gluttony should only keep two sets of move set of it's victim, one from the last champion it consume, second from the last minion it consume. This way, it will only have 2 sets of movement at the same time, preventing it to be overpower at late game if it consume many different units early on.

As for the idea of being able to kill own unit, this should only be available after Gluttony gain move set from consuming enemy's unit. As time goes on, the lust of eating grow and Gluttony starts to consume unit from it's own side, becoming cannibal.