An analog wall clock to be programmed

What you want is basically already available as a 15$ kit (to assemble yourself), only with a slightly different behaviour. I could buy this kit, build it, reprogram the microcontroller and ship everything to you, but I think the best way forward is for you to buy this kit and build it yourself (it's rather fun, you only need a soldering iron); and then I can buy a replacement microcontroller, program it with the desired behaviour, and ship it to you for direct drop-in replacement. If you would prefer me to build everything for you, bear in mind that the price of the kit and the shipping costs to me, and then to you, will be added to the bid cost (estimated: 40$ additional).