The American republic has often been compared to the Roman republic. You are doing that here, and if history repeats itself, what you are proposing will lead to the fall of America – not its renaissance. The divorce and division of the Roman empire into east and west defined the empire’s decline and preceded its dissolution. Many saw it coming, many feared it, many welcomed it; but regardless, it was inexorable.
It is ancient wisdom that to understand a problem is to understand its solution. You have adequately analyzed America’s problem: Loss of comity, if we ever had it. Rome, too, had that problem. What united the original republic ultimately tore it apart.
In America, the disparate several states united to create a United States of America. Factionalism, which the Framers warned against, is rending us apart. You hit on the truth that we are divided along myriad lines, but it wasn’t always so. The two-party system served us relatively well for over two centuries, but no more. Our socially world-wide-web has exposed our differences as never before, technology magnifies issues exponentially; there is no going back. Our duopoly is obsolete.
The problem is graphically depicted in your map: Republican, Independent, Democrat. But graphic too is the fact of that commonality regardless of the geographic region. Yes, more or less, but still present. We are self-sorting all across the country; ideologically more so than geographically or even generationally.
The solution is also graphically depicted in your map: We need three parties, not two. We need a conservative, a moderate, and a liberal party. We need a transitional solution which will utilize our diversity to reunite us. There will be no constitutional amendment such as you, or anyone else, can propose. But the default position is illustrated. Three parties of rough parity; enough to shift to right, left, or middle as the case may warrant. Two divisions of which would constitute an overwhelming two-thirds majority consensus, no doubt with some compromise and moderation along the way.
The “massive public support” you seek, the Fifth America, may be right before your eyes.