EDIT (2/10 3:56PM): The Thingiverse Customizer is being cruel to me today, I have no earthly idea why, but when it renders my object it screws up the tickmarks for the hours and minutes of the day. I'm going to keep banging my head to try and figure it out, but until I do please download the OpenSCAD file and customize to your heart's content, it works perfectly fine.
I wound up doing some work to record better time-lapse recordings of my 3D Printing activity (for more detail see: Integrating my 3D Printer into my Home Automation) and realized that I wanted an analog clock in my time-lapse videos to give the viewer an idea of the amount of time that passes during a print.
Buying a clock was far too easy, so I decided to go ahead and design my own! I picked some clock guts off of Amazon and designed a clock around the gearbox that I bought and some other design elements.
I was pretty happy with how it turned out, my first video turned out well enough that having designed it in OpenSCAD, it only made sense to take the design one step further and turn it into a customizer!
To avoid some of the hassle caused by the bevel on the backside of the clock, I went ahead and split this in two pieces with the intention of gluing the pieces together.
Before doing any gluing, test fit everything together; the clock face, the clock's backside, and your clock's guts. If things are close, I'd suggest using a file to make the holes bigger for the pegs and/or the clock's guts.
Assuming everything fits well, I suggest putting the pegs in the clock face by using a little bit of superglue. Once the pegs are dry and in place, put a couple dollops of superglue in each of the pegs' holes and maybe one or two more on the clock-face's rear. Press everything in and let it dry.
Once it's dry, you should be able to put the clock's guts in, get things affixed. To hang mine on the wall, I wound up adding a 1.5" picture frame hanger. Perhaps designing one into the object is a good next revision?