Back to basics. Since you are not a telephone technician, I will state the questions, and you will ask them of the carrier who supplies your POTS lines. You don't need to know why we are asking the questions, until we get some answers. Then we'll let you in on the secrets of copper telephony.
Suffice it to say that we here on this Forum have little confidence in the training and abilities of many field technicians now employed by LEC's.
If, while questioning the technicians, you get eye-shift, lip-licking, stammering, or any other of the classic symptoms of untruthful answers, (I used to work for the Navy as an interrogator of criminals for the USMC) ask to speak to the oldest repairman in the area. He will understand the questions.
What voltage and current measurements does the LEC read when they test your POTS lines from your location? The correct reading will be 48 to 52 volts DC on an idle line, and about 25 mA or a little more, when a standard telephone is off hook.
Are they copper all the way from your location, back to the serving CO? (This is a critical point. If they are NOT, then disregard all that follows.)
If so, do the pairs have bridged taps at any location?
Can/will they clear the bridged taps on one line to see if that clears the problem?
Are the pairs loaded?
Can/will they unload one of the pairs to see if that clears the problem?
Do the pairs test absolutely clear from any metallic faults? Have they stress-tested the lines?
Do the repairmen see any bridged (left-in) stations when they test the lines?
What type (manufacturer and model number) of Network Interface Device (NID) is installed at your location?
Are they willing to bypass the NID temporarily to see if that clears the problem?