I would suspect the actual problem is at your exchange or to do with the phone lines to your property.
Don't know where you live but many places are still using 'old' wiring that just simply can't cope with the amount of traffic that it's being subjected to.
I had very similar issues with my phone line and broadband for two years until some clever engineer fixed it.(8 or 9 had tried doing all the things that you described with no joy) He decided to swap our lines at the exchange to avoid going through some old wiring in the road about 300m away. All of a sudden problem solved - no noisy phone lines and constant broadband. Hope you can get it sorted.