Sounds like you've done everything you could to salvage the lights. It is time to either remove and replace them or buy a new tree.
I've considered buying a pre-lit tree. I've got an artificial tree I've used for 10+ years and strung the lights myself, keeping them on the tree between uses, and have had few problems. From what I've read just now, pre-lit trees are intended to last three years (unless they have LEDs and then the expectation is longer, although LED light strings can have problems too).
It appears that most manufacturers wind the strand around each branch, much as you would if you were stringing them yourself. This can lead to wire breakage as wires age, plus the stress of setting up and storage. Some sites I've read going through your problem did exactly what you want to do: remove the strands and put new ones on. It should be more time consuming than difficult. If you don't want to try and save the dead strands I would suggest UNPLUGGING THE TREE first, then using wire snips to cut off the dead strands.