You might want to post on the photography side as well. This is old school. There might be something newer than 1970's methods.
There is a product called dry mount tissue. It looks and feels much like wax paper. Used to mount photos permanently to mats for display and is heat activated. The paper is thin and can easily be cut to shape and fit beneath the clock face (best if in one piece to prevent lines in the surface once heated for permanent placement). With a dry mount iron it can be loosely attached and adjusted to fit. Once set loosely in place it it is set to the substrate. This can moved for placement positioning. It is then ironed from the face. This is temporary until the whole is firmly and permanently attached as a sandwich---clock face/dry mount paper/substrate after being placed in a dry mount press.
The whole process should take less than five minutes. It is equipment heavy and experience based though.
Caution because it is heat sensitive you have to be aware of what you are doing. If it is too cold the binding won't work. If the heat is uneven or too hot it can darken the showing (clock) face. If the iron itself is dirty it can leave a permanent mark on the top item (clock face).
Any art frame shop or graphics house has the supplies and the equipment. One important piece is a dry mount press. To have them do the work would not be expensive, and they ought to know how to do it. If you have never done it before have it done. Ask around to be confident.
You tube has more than a few videos on the process "Dry Mounting Photos" -- take your pick.