Thank you for describing the current situation.
The coupling between your circuit and that of your two neighbours must be taking place within the common, multi-core cable. To replace each individual service feed with either Cat5e or Cat6 cable will not help. At best all you will gain is the knowledge that the wiring is new, with freshly made connections.
I presume your neighbours see a similar effect, with your modem being a source of NEXT to their circuits.
I wonder if the three circuits are using individual twisted-pairs within the multi-core cable or, possibly, there is one or more cases of split-legs.
If you have not already done so, could you and your neighbours contact the service provider and arrange for them to visit all three of you & to perform some tests?