At Hashnode, we faced the same situation six months ago. After a lot of discussion, we decided to migrate the app from Alt to Redux, in a gradual fashion. The reason behind the gradual change route was simply this: a complete rewrite would have taken a lot of time, and we didn't have that luxury.
We are a small team. We have to push new features, fix bugs on a weekly basis. With that, writing a brand new app would have been impossible. It took some time to make the existing Alt part play nice with Redux, as we have to keep Alt and Redux stores in sync, at a few places. But, this approach worked out well for us. As of today, most of Hashnode is in Redux.
If you have the time and resources to write the new app, a complete rewrite would be a good idea. Otherwise, the hybrid approach is your best bet. Let me know if you have any specific questions.