The big issue with Greater Good is drawing too many cards and thus losing the game. Can I perform the combo without letting any Greater Good activations resolve?
Yes. The key point to remember here is that you sacrifice the creature as part of the cost of activating Greater Good's ability, so before it resolves (remember that under C.R. 602.1a, an activation cost is "everything before the colon" of an activated ability). If any abilities trigger as you pay the cost of that ability, they will go on the stack above Greater Good's ability (C.R. 405.2) and get to resolve before it (C.R. 116.4; see also C.R. 116.7). This includes triggered abilities such as that of, say, Pattern of Rebirth. And any abilities that trigger while those resolve (such as those of Karmic Guide or Boonweaver Giant) will get to resolve before Greater Good's ability, and so on.
If you're unfamiliar with that combo, see here.
The big issue with Greater Good is drawing too many cards and thus losing the game. Can I perform the combo without letting any Greater Good activations resolve?