The primary issue sounds to be very high attenuation due to a long line. When a line is unstable, tweaking the signal to noise ratio margin can sacrifice speed for increased stability - but the high attenuation means you have almost nothing to sacrifice in the first place. BT getting sync when they tested the line is a relative red herring, especially if this test did not stretch over several days. The line sounds just too marginal to be reliable, especially if the 0.13 speed (128kbit/s?) was the downstream sync speed when it did sync on the test gear.
Unfortunately your remedies in this case are very limited. DSL is a 'best efforts' service; if the line cannot reliably hold sync, your remedy is limited to cancellation of service and almost certainly a refund for the period when the line didn't work. The sub 1Mbit/s predicted speed should have alerted you to the possibility that the line wasn't going to work at all, but I appreciate that there's a big difference to you between a slow connection and no connection at all, also you might not have appreciated that such a low predicted speed means the possible outcome is no service.
It sounds as if you are outside the footprint of any BDUK funded fibre work as you have been offered a voucher for satellite. Unfortunately, I think you are in a location where wired Internet is not available. I'm guessing Quickline is fixed wireless - and if they cannot offer you service because of obstructed line of sight, your only options are mobile, satellite or bringing an alternative service to a location from where you access it over Wi-Fi (which might just overcome the line of sight barrier at your location).