My personal favorite approach would be via Red Revolution--the Social Democrats take over. The approach would be via more absolutism, not less, and right-wing political leadership screwing up stupidly, thus forging a Liberal/Left alliance.
When the dust settles, it might still be a constitutional monarchy--I said SDs "take over" but I'd happily settle for them being just a crucial and indispensable part of the winning populist coalition. It might be like Weimar but with the regime having the legitimacy of a victorious social revolution rather than appearing to be the product of foreign intervention. And it would start earlier and last longer, maybe indefinitely.
Having the crazy right wing remain rather strong in electoral terms might stabilize the role of the center parties--the Catholic Zentrum itself, but also small liberal groups--striking the balance between monarchists and more rabid proto-fascist rightists, and the Marxist socialist ambitions of the SDs, who in turn would probably prefer to tolerate a humanely regulated capitalism under the stewardship of the middle parties (who listen to them if they want to stay in power) rather than risk the rightists taking over.
That pretty much was Weimar, at its best.