TBH, re-locating the existing line alongside your newer 2nd line, would literally be an extra 10-15 mins work.
The cable that would be cleated from the BT66 to where the NTE is required, can carry two lines. So, it would just require the engineer to put 2 NTE's side-by-side at the new location.
Tea, biccies, bacon butties, bottle of cheap plonk (individually, or a combination of) ….. are all good starting points
. Plus, "Is there anything I can do to help you", always endears me slightly more towards the EU and efforts put in, above and beyond.
So, I would go for it, and hope you get an OR engineer. If it's a Contractor, you may need to slip them a tenner to re-locate the existing NTE. Just my thoughts, as everyone works differently.