I hadn’t seen that ruling. It looks to me like the ruling it links to has been superseded/clarified by this bit of the FAQ:
When a card has a trash ability that is triggered, any reference to the game state within that resolving effect is based on the game state as it was at the moment of trashing, but with the trashed card considered a new copy of that card in Archives or the heap.
That section only talks about trash abilities, which I believe means cards that trash themselves as costs. But in the absence of a separate ruling about cards that trash other cards as costs, I think it could be argued that it applies to those too.
If that’s the case, then you can break a sub with a Lister-boosted Faust even if paying the cost causes Faust’s strength to drop below the ice’s. But I don’t think you can break another sub after that, because that would require using the sub-breaking ability a second time after the strength is too low. I don’t think you can even try to trigger the ability again because it has no potential to change game state.
(The original ruling is also in response to questions about cards that are trashed while abilities on them are only partially resolved, but I don’t think that applies here.)