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I don't think the mainstream Democratic Party is as "Far Left" as you seem to think. Sure, there are some progressive "stars" like the gang of five in the House. But almost half the House is pretty centrist. On the other hand, pretty much all of the House Republicans are Trump supporters. The moderates are most Lincoln Project supporters. Rare as hen's teeth.
So I think your ideal "Centrist Party" does already exist, and it's called The Democratic Party.