Hi all, the transaction got confirmed sometime during the night. When I woke up it had already 13 confirmations, so that's that.
And yes, I guess it was not fault of Electrum but a series of unfortunate events that happened exactly after I sent that transaction which lead to it getting stuck.
But the good news is, the site I sent it to credited my account, even though the transaction came in very late. So, everything went well in the end.
Thank you to everyone for replying and sharing their knowledge on this matter. I really learnt a lot about mempool and how and what gives transaction priority.
I suppose the only certain way of making sure that your transaction gets accepted as soon as possible is to keep overpaying the fee.