I assumed their plan was to have such great volume that they'd eventually be able to negotiate (larger?) bulk discounts with theater chains and thereby get their marginal profit back above zero.
Agreed. Somehow, they need to get the theaters and/or the studios to share in their model.
If they can demonstrate to the theaters that their heavy users are worth a lot more than just a ticket, perhaps high concession sales (through coupon redemption), then maybe the theaters would consider giving them a break on ticket price because they're supplying high-value customers.
Secondly, if they can pump the hell out of new movies so the studios or distributors get an even bigger bump on opening weekend, then the studios might be willing to fully or partially fund those tickets for that publicity (aka "trade spend").