I am sorry for your problems, We lived in a flat once with a upstairs who was a problem. Happily he was a little chap and my DH while a peaceable man is built like a rugby player, as are many of his friends. It only took one friendly conversation to nip the noise in the bud but I do sympathise. Might the local council be more interested if you mentioned involving the police? I am assuming that you have proof of the threats? and have kept the rude notes and you can prove they wrote them? Your local Citizens Advice Bureau might be able to help you sort this as they will know local methods and contacts. In law renters do have a right to "peaceful enjoyment of the property"but the remedy is usually against the noisemakers and not the landlord.
If you do go this route, it won't help with the landlord, I am afraid and if he knows upstairs are hellions, he's going to want to hang on to your cash as he might not let again so easily. basically cut and trun might be the least stressful, it depends how much of a fight you want