I had the same split valve stem issue, and I had the same thoughts about the same replacement tire... but I was too cheap to do it, and just replaced the valve stem with one from Autozone. I have a spin balancer in the garage, so it's DIY either way.
I'm sure age isn't a good thing for the rubber, but old tires actually mounted on cars and exposed to sunlight seem to have a lot more problems with cracking and other obvious deterioration.
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