At least they are keeping you in a skilled job!
I'm curious, how do you know it is the coil and not the circuit driving it? (don't tell me, you've seen the same fault many times...)
It usually gives a fairly unique fault symptom, something that can't be caused by anything else - as I said I've only ever seen a couple of failures, and I didn't waste time looking for anything else - it just screamed 'scan coils' at me (even when I've never seen one before).
The problem now though, is that CRT's have been PIL (Precision In Line) for decades, so there's no adjustments, it's all done during the manufacturing process, I presume by actually altering the scan coils to correct convergence and purity. The exception was Sony, who never made PIL tubes.
So tvtech was pretty well stuffed, no way to do a decent job - and as he said, accept it, or bin it - the 'proper' way to repair would be to fit a new CRT, but it's unlikely one would be available, and it would cost more than a new TV anyway.