Noting that your local shop used wires because that was what was available ... but the default recommendation is for a strap type clip as you've found.
Thanks for the drawing - and yes, inner grove is noted; oddly there is no outer grove.
As to the shop - it was a rare wrong call: the car (very original, mostly) came in with wire clamps so they did the same thing, trying to keep it as it was. They recognize this probably was an error and will fix shortly.