I often need to quiet a mechanical pump to prevent interference with acoustically sensitive lab equipment. The solution is placing an enclosure over it, made with some light MDF and lined with sound deadening material. (In the case of the pump, they also put out a LOT of heat so a vent and small fan must be added, but not necessary in this case.)
You can buy inexpensive sound deadening material with adhesive backing to make one. Also, the chime box is bolted to the bottom of the cab, so that must carry some of the initial strike sound, so a rubber mat under the box would help.
Try placing a cardboard box over the chimebox to get the idea what I'm talking about.
Oceanside, NY
