Anyone found a new way to clean up sick glass?

[Paper Roses]

The charity I volunteer for just received a beautiful cut class carafe. The glass is sick. I am authorized to take certain items home for a better cleaning than we can give items at the shop. I have tried everything except CLR. Something tells me that would be a waste of money. I am not reimbursed for supplies.
I am willing to do the work but do not want to waste money. The neck of the carafe is narrow, I cannot get any brush or compound inside. Whatever I use has to fill to the top of the carafe and soak.
Any ideas would be appreciated.