In your position, I'd go with Myth's suggestion - order FTTC, possibly with a different provider.
TalkTalk are clearly not interested in the original issue. Judging by the wording of your speed test result and the use of G.DMT on a line that looks as if it could manage much more on ADSL2+ (MrSaffron's calculator estimates up to 19.5 Mbit/s downstream at that attenuation
), I'm guessing that your current service is over BT Wholesale 20CN. If that's the case, it would be interesting to know what the PlusNet exchange status checker
says about 20CN VP capacity. The issue sounds more likely to be backhaul congestion than anything to do with your line, considering the time correlation, low attenuation and healthy noise margin but without error statistics, it's impossible to be sure.
If the only ADSL available is BT Wholesale 20CN and the backhaul VPs are congested, every ADSL ISP will suffer the same issues. Rather than waiting around in the hope of the obsolescent 20CN being upgraded, I'd defect to FTTC which uses an entirely different setup other than the same wires between you and the cabinet. As Myth says, you also have the advantage of an engineer install with FTTC. Especially if you get a BT Openreach engineer rather than a contractor, there's a good chance of any outstanding issues with your line being resolved at the same time.
If you're leaving your current setup behind, I'd just put up with it for the next few weeks - it isn't worth the hassle.
Considering the (lack of) customer service you've received from TalkTalk, this suggests you may want to look elsewhere for an FTTC ISP.