Booking date change difficult due to technical problems, who is liable? [closed]

Short version: I tried to shorten an existing hotel reservation, booked and prepaid through a large travel site, a day before the "free change/cancellation" period runs out. They tell me the hotel has to manually make the change in its system before the request can be processed. What happens if the hotel does not confirm the change before the free period is over?

More details: I booked a hotel stay for 9 days through a large travel site. The rate includes free booking changes or cancellation up to T-1 (where T is the date of arrival at the hotel). As I am arriving tomorrow, that means I have until midnight tonight. Realistically, it is until 19 PM, since my overnight flight takes off then.

Now I have to shorten my stay, and will only be there for 5 days. However, I was not able to make the change either on their website, or through the customer hotline. The reason given was that their system actually frees the booked room and books another one, but there are no free rooms left in the hotel.

I tried the change yesterday, and the hotline person told me they talked to the hotel, and the hotel asked them to do it over email. Today I called again, the hotline person contacted the hotel again by phone, and the hotel claimed they had not received the email, but that the booking company should send them an email again and they will reply promptly.

I asked repeatedly what will happen if the hotel does not reply before my cancellation period is over. The hotline person always answered with "not to worry, the change will be made once the hotel has replied". I asked for a written confirmation that my reservation will be changed, all I got was a copy of the email the hotline person sent to the hotel. It is at least proof that I requested a change within the proper period, and contains the dates of the rebooking.

If I don't get an answer before I fly, I have two options: rely on them that the change will be made and the last 4 nights will be refunded. Or cancel, and get a full refund for certain, and book another hotel. While other hotels are available at a reasonable price, I have a strong preference on this one, since it hosts the conference I am visiting, and travelling between the conference hotel and another accomodation after dark might be risky (the city is not completely safe).

So, what am I asking: with that email (which is proof that I requested a change within the period in which I am allowed to change for free), am I entitled to a refund, regardless of how much the hotel tries to stall? Or is it that once midnight comes, everybody can wash their hands and I can sit on a payment for 9 nights even if I only stay for 5?