The worst way to communicate about an issue such as this is by email and the worst subset of this is with generic customer service.

When a problem such as this arises, one needs to establish a human connection with someone in authority at the property.

"Mistake" fares and rates are far from clear in both the US and the EU, so not worth arguing about that here as any legal solution will not affect what you need to do now.

I would call the property during regular US business hours today, e.g. right now or wait until Monday. Ask to speak with a manager and explain the problem. It is highly unlikely that you get the room for $15, but entirely possible that the Manager agrees to a reasonable rate that you are willing and ought to expect to pay for the room, even if that rate is not now available. The key here is that it took the property 6 months and you have booked other non-refundable rates in the meantime.

I don't think that it is reasonable to have presumed that the $15 would stick and the fact is that had you called in before locking in other expenses, you would have received a quick answer. If indeed the rate was for real, you would know and if it was a mistake you would know and could act accordingly. But, any property would sooner or later catch the $15 and, if a mistake, deal with it.

For what it is worth, the US rule for air tickets (guidance not a formal rule at this point) from DOT (which has no authority over hotels), is that a mistake fare may be cancelled, but the air carrier must reimburse any fixed costs incurred by the passenger in reliance. Thus, in your case, the property would have the option of either leaving the rate at $15 or covering the non-refundable costs (when you provide evidence of cancellation). But, this is air fare and you are dealing with a hotel.