Your musings on the subject of political parties, not to mention your frustrations, mirror mine in many respects.
I will say, though, that I am not against convening a new Constitutional Convention. Thomas Jefferson believed that the Constitution should be re-written every generation to conform to the demands of a new political reality. Of course Thomas Jefferson wasn’t that big a fan of the Constitution at the outset, so grain of salt and all that.
The founding fathers definitely weren’t big on political parties. The problem is that they were really mapping new territory with the Constitution and most of the document was based on a bunch of really smart guys theorizing about how the ideal system would work and then wrangling compromises to get everyone on board. Some of these compromises still seem pretty good, like the House of Representatives and Senate and how seats are apportioned. Other compromises were pretty awful, like the Three Fifths Compromise.
The real problem remains first past the post voting. Every single time we’ve seen an election with more than two candidates getting a percentage of the vote worth talking about it’s marked a time of flux in the country. 1824 marked the end of the Era of Good Feelings, when we did have a single political party, and the transition to the Jacksonian era and the move from republicanism to the Imperial Presidency. 1860 was the Civil War, of course, but that was marked as much by the split between Northern and Southern Democrats as it was the rise of the Republican Party. We mostly shorthand the election of 1912 as Teddy Roosevelt throwing a temper tantrum, but that stretch was a major sea change in America, as we were facing the transition out of the Gilded Age and into labor unions and protections for workers and trying to answer the question of how much involvement the government should have in the life of average Americans. Hell, Eugene V. Debs almost got a million votes running for the Socialist party that year.
The thing is that each place where there are more than two parties worth talking about usually marks a breakdown in the coalition for one party or the other (1892 being a bit of an outlier, as the Populists have always come off as a genuine grassroots opposition party to me). 1824 was all about the general implosion of the old Democratic-Republican Party. 1860 was about the split of the Democrats along Northern and Southern lines. 1912 was about the split between the progressive and conservative wings of the Republicans. Hell, even Ross Perot was a bit of a canary in the coal mine for the Tea Party and various bits of Republican weirdness that’s taken over the party.
The problems always go back to first past the post. Whenever a new faction arises it’s either given sway or it splits off and takes its part of the vote. The vote tends to be somewhere in the neighborhood of 50–50, so a good chunk of a party splitting off pretty much guarantees the other party gets the nod.
We don’t have to go full parliamentary, but I think we do have to look at reforming the way we determine winners. Instant Runoff is a popular alternative. I know that Direct Party and Representative voting is potentially great for parliamentary systems. I don’t know if it will work in our system, though.