Right, firstly I'm going to have to ask that you forget what other engineers have said. I wasn't there, and so don't know what context it was said in, or whether you have inadvertently got what was said wrong.
Not a pop at you, but if I'm to give advice, I have to as if I am approaching the task
myself for the first time, without any other input from 3rd parties.
Then, you can take what you want from it, and make an informed decision as to how to progress ?.
To clear up the FTTC confusion first. Generally, there will be two Cabs where FTTC service is provided ..... the original where all the wires from various DP's meet the wires from the Exchange ..... and a newer secondary one that houses the Fibre BB equipment. They are supposed to be within 50mtrs of one another, but can be more if required to, so have a look around. Failing that, you may belong to an extremely rare beast known as a 'Combined Cab' the clue's in the wording.
To put the distance issue to bed once and for all. You are on a long-line but
only where Copper Broadband (ADSL) is concerned. ADSL sees the broadband equipment housed at the actual Telephone Exchange, so 6.8Km is a long way to travel for the frequencies this type of circuit utilises ....................... but, it is
NOT a long way for the far, far lesser telephony (Voice) frequency.
As an aside, I've calculated that your circuit equates to roughly 11.7dB attenuation at 1.6khz (Voice), that said, I have no idea of your circuit make-up in relation to type and size of cable ?. Automatic 'Gain' on the telephony equipment only generally works up to approx. 10dB, so you will have been put onto one of the manual gain settings, of which your circuit would fall into the lowest of these settings. I can only assume that the OMC (Operations Maintenance Centre) may have tweaked the gain up to one of the other manual settings, designed for much longer lines ...... but to no avail ??
So, all-in-all you are
simply stuck at present with a (To use your own deduction) ...... 'Both-ways faint transmission circuit'. No need to mention broadband, or long line etc, to the call-centre advisor or the visiting engineer. As I say, it only serves to throw spanners into the works.
If, as we assume, the pair-of-wires from the Exchange to your house test perfect (via the PQT) ....... then to my mind it can only be something 'Plugged in' at either end .......... ie: The phone or the actual Exchange telephony equipment ?? You say you have ruled out the phone ........ so .........