Best offer is the clue – I think eBay gives you a chance to come back to the buyer with a counter offer but I’m not sure the seller can stick another best offer in – that might be the issue, otherwise you jst end up with a string of ‘how about £10? How about £11, how about £12’ etc.
If you commnicated with the buyer using ebay then eBay may not be too happy you cancelling the auction if its obvious you’ve made a deal – its outside their terms and they may take their fees anyway. Might get away with it though.
Photo of the buyer and you/the goods might be enough if they still want to go the paypal route – cash effectively removes their buyer protection so its more of a risk from their side dont forget.