Well, you could go to an independent watchmaker and get an assessment of what is wrong. If no parts need to be replaced, he could fix it for you. Still, he would not make much money on just that issue so he wouldn't be much interested in the job. He takes a certain risk (there is always the possibility of something going wrong during servicing, needing parts replacement) and gets virtually nothing for it.
That watchmaker might offer to do the whole watch for you (at eight years, it's about due for a service anyway) but he won't have access to parts and a full service would cost a decent amount even at an independent watchmaker.
You could send it to Zenith and just ask them to fix this issue. A partial service at Zenith still costs a decent amount so you might as well go for the full service.
But then, you seem to have decided to do the right thing already.....

Zenith cost a fair whack but they do a good job. I never had any problems with them.
Hartmut Richter