I don't think it is necessarily unreasonable for them to ask you to return the goods at a time which allows them to deal with it there and then. I certainly am not aware that they have to be able to comply at all times of day and night, so yes, I'd say they can say this, or at least they're not breaking any law or denying your statutory rights by doing this.
And secondly, yes the 6 months reverse burden of proof runs from date of
original purchase, which I agree is ridiculous, but is exactly what happened to me with a laptop, which is why I know the answer. so no, you're wrong.

The onus is on you.
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