So I asked if maybe you were referring to a Marxist overthrow of the capital-owning class.

Yeah, basically. I was hoping to qualify my statement with "well, I pretty much believe all this, so if you want to argue it look there first".

I don't see why there's not multiple routes to that end, or why there's a reason in principle that that sort of agenda couldn't be enacted via popular vote, as opposed to a violent overthrow.

It's a pretty wide argument, but basically the Marxist view is that classes always seek to retain power. Except in a very small amount of present-day democracies, virtually the entire state is run by the capitalist(aka company-owning) class, regardless of how open the elections are. This is called a bourgeois democracy, and like all other forms of capitalist-dominated government it will always seek to keep the capitalists in power, regardless of the true wishes of the people. Thus, if the people get too uppidy, they will simply shift gears and try to appease them without giving up real power, like FDR did. You'll notice, none of FDR's reforms fixed any of the underlying problems with Capitalism, they simply made them less obvious for awhile until the capitalists rolled them back or found loopholes. Reforms have proven to be effective only in relieving some of the short-term burdens of Capitalism; they have never done anything to fix it. Social democracy does nothing long-term to fix Capitalism.

And now you will say, "well, revolutions haven't done much to that end either". I respond with the point that it all comes down to the Russian Revolution. That one revolution, in 1917, set the stage for all socialist revolutions that followed. And, as we know, it didn't go too well. It's unknown exactly why, but it's a common sentiment on the left that it was caused by a combination of military and economic external pressures in the early years, which caused internal strife that the Bolsheviks used to move power away from the Soviets(worker's councils, the basis of socialism) to the central government. Thus, you end up with strongmen like Stalin and Kruschev who ruined the dream forever.

Even so, in most cases socialist revolutions have made big changes for the better. The standard of living in the USSR shot up in the 50 years after the revolution, and that was concurrent with three invasions and a civil war. Cuba used to be your average poor island country, and now it has a literacy rate of 99% and some of the best healthcare in the world. Seems to me it's the only way to go.