Ok the pragmatic choice is to just lie - I would wholeheartedly lie to my parents if the same situation happened to me, if I was in a deep, troubling situation like yours - And I'm good at lying. The ethical choice is to not convert and search for a new house. I don't know where is the love between parents and children when they make these ultimatums.
Whoever fights monsters should see to it that in the process he does not become a monster. And if you gaze long enough into an abyss, the abyss will gaze back into you