In robust language, they demanded a refund by Paypal. So I tried to initiate the refund

Unless they provided evidence in the form of photos or a condition report why would you initiate a refund?

Six weeks is 42 days, if they haven't already opened a dispute another three days and they won't be able to so I would just try and keep it going until the 45 day limit is reached.

If you are a seller then you are meant to have a bank account linked to your account anyway as that is the only way you can withdraw funds so it is hardly Paypal's stupidity.