Why not both? It's easier to force your way under and into that tent/coalition with an organized front to do the talking. A political party that has well defined goals and objectives, while speaking for a big group, is bound to be better at working within a broader coalition than what we have now.
Only Democrats are allowed to vote to elect Democrat leadership... Need everyone in that coalition to register Dem and then vote for new leadership... 3rd party will always be spoiler until we take over and unrig everything
Fine, then it's not a political party outright, and instead a lobby. Or a trade association. Or a big bunch of very angry like-minded voters. The point is that such a group could exert leverage within the DNC coalition as a voting block. We already have these for other interest groups. DNC membership is really only useful for voting in primaries to most people anyway - it doesn't have to signify allegiance or kow-towing to party power.
That would be ideal, but the people who are already there will never give it up.
And the problem with creating a new party is that it will divide the votes, while the conservatives are all united under the Republican party. Unless they split too. Maybe the non Trumpists can split off and form a more traditional party. But again, they're too afraid to split THEIR votes.
Party leadership is elected by regular party members at the state level, and then those choose the national leadership (oversimplification)... I'm sure the current leadership would fight back, but I don't think it would be all that hard to vote them out anyway
A reverse tea-party movement. That could work. We were laughing when the tea party started because it seemingly broke GOP unity, but they managed to shift the Overton window so far to the right that the GOP now is the tea party, and Dems are GOP lite. Reversing that trend is extremely necessary.