Test test socket is still the boundary.
If you cancel you will be left with FTTC at 16 Mbps, now it may be the line is back to its proper state but the DLM has reacted to the noise and errors during the fault and when the rewiring took place and has slowed you down.
In theory if an Openreach broadband engineer looks at it and decides a reset of DLM is best as a fault has been cleared then one can take place. NOTE: The IP Profile is just the visible effect of the DLM and sync speed that modem ends up negotiating so resetting IP profile will not help, unless the DLM is reset too.
Really unsure why the BT operator is almost threatening with the bill, test socket tests usually mean you are fine, unless it turns out the fault was a strimmer having a go at the line and someone has quietly fixed it or similar.
A migration on the way should not change anything at all in terms of line performance.