I am glad that you liked it. That page has a several interesting things. Some time ago I picked up a similar clock for a few bucks but I did not restore yet it because beside the 50/60Hz problem it has broken "leaves". It seems that the plastic got fragile with the years and the little tabs that keep the numbers in place got damaged. I need to figure out a way of repairing them.
Question: Is the power consumption listed on the back of the radio? (to know sizing requirements for the mini-invertor - if you so decide..)
Only the small synch motor needs to be fed with the 60Hz sinewave, that lowers the power requirements for the inverter. Then you can replace the original 110v power supply transformer with one for 240v. May be a little bigger to drive the radio and the inverter at the same time.
A little more riskier approach is to put a suitable capacitor in series with the primary to reduce the voltage to 110v. In this case the voltage may vary when the radio is ON but probably that wont be an issue.