I don't remember what I ate last night
but I can spout off obscure rules to all sorts of game like nobody's business!
When you need more cards, you need to take them from the 40 cards that were removed from the main deck. That means that you only pull from the 40 card deck once so that you won't actually play through that entire second deck. Is that correct?
In phase 1, if you're dealing from the set of 40 cards that were set aside earlier, that will be the last turn of the game. You don't have to deal all the way through those cards to finish.