Technically, yes you are required to have a ticket out of the country within 90 days of arrival unless you already have your residency visa in hand. I’ve never heard of Ecuador refusing entry into the country without it, but some airlines will prevent you from boarding your flight if you don’t have a return ticket. I believe this is because if Ecuador does decide to block your entry the airline is responsible for sending you back home.
Orbitz often has a two-day cancellation policy without charge, so you could book your return flight just before leaving for Ecuador and then cancel once you’ve arrived. American Airlines used to have something similar as well, but I’m not sure if they still do.
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