Just a Thought:
The more I look at this pair of Lady Ks, the more I'm taken back in time. One of my high-school teachers used to sponsor student events that were held at her parents' house; they were quite wealthy people. Their kitchen was outfitted with the latest and greatest Kenmore everything, in coppertone. Off the kitchen, there was a laundry alcove, equipped with this identical pair. The kitchen was papered in a brown/cream/red plaid, even on the ceiling. For the late '60s, it was some punkins.
I had a thought about your timer cam drum, based in experience with broken gears in Volvo speedometers. Plastic parts of this kind can be machined to order; Delrin is the usual plastic of choice for the purpose. It costs a bloody fortune, but it can put an obsolete part back into existence. While you're good for right now, this might be a good thing to remember if you run into repeat trouble (God forbid!) later on. Any good machine shop should be able to advise you on this. However, when I said expensive, I wasn't kidding - it would be in the hundreds for something like that, because it's all precision work, much of it done by hand.
A Lady K matched pair would be worth it, though.