There are several things you can do. The use of a cleat glued to the back as mentioned above would work. Adding a backer board will also thicken the piece.
You can also mount your piece to a picture frame and use the hanger that comes with it.
You can use a D ring type hanger glued with a product called E 6000. It is a thick adhisive that bonds anything to anything. I use it all the time without any failure. You can find it at any craft store.
Lots of ways to do it!
I suppose that would work where space is not an issue. Here in So. Ca. You usually have a 10'x10' space. If you need more, you have to pay for two spaces.
Neat idea though.
Edward, when I teach new students, I start with 3/4" pine and an Olson #5 skip tooth blade, but at home, I would use an FD UR #5. 3/4" poplar is not very hard, so #5 should do you well.
Nice looking clocks JT! I have done some of those from a plan in Wood Magazine.
I have scoured all the sites I know of that sell fit ups with no luck finding what you are looking for.