Try the horse hair cloth if you wish. Its the cheaper method, but with the less possible success.
If it does not work it can be removed without damage. but you pay for both the doing and then the undoing.
TO do the major alteration, you must have at least 3/4 of an inch of cloth available beneath the collar.
Thats right there at the curve of the gorge,and up to the shoulder seam line.The measure is along the
shoulder seam line.
. Your tailor will need to break a few stitches to peek inside.