What would democracy without capitalism look like?
I imagine that it would look like democracy. Unfettered capitalism and democracy are innately incompatible, since democracy is all about diffusing power among the whole population, and capitalism concentrates power into the hands of a few.
The notion that democracy and capitalism are innately incompatible is rather interesting, given that every long-running democracy has a predominantly capitalist economy. There has never been a durable multiparty democracy with a state-owned or centrally-planned economy. Not one! There are several examples of non-democratic nations with capitalist economies, but the complete lack of any successful non-capitalist democracy argues pretty strongly that capitalism is a necessary (though not sufficient) prerequisite for a healthy democracy, which is the opposite of incompatibility.
I did note that you attached the qualifier "unfettered", but has there ever been an example of unfettered capitalism? I'm not aware of one, and it seems fundamentally impossible. Capitalism requires a state to enforce property rights and contract law, and it's hard to think how any state could exist that does those things but doesn't also impose some regulation. If by "unfettered" you mean "lightly regulated" rather than the literal meaning of the word, then it becomes a question of degree but democracies have gone through many cycles of liberalizing and regulating without ceasing to be democracies.
As for your assertion that, "Democratic socialism always ends up quickly abandoning either democracy or socialism." I assume that you're talking about revolutionary governments.
No, in fact most attempts at democratic socialism have been entered peacefully. They tend to begin by election of a socialist leader with enough support to begin nationalizing all or most industry. Examples include the Allende regime in Chile, India's government for much of the latter half of the 20th century, Sweden's Meidner Plan, Venezuela (Chavez' second attempt; his first try was a coup but then he was elected), etc.
Socialist revolutions almost always install non-democratic regimes, though many claimed to be democratic (e.g. the USSR had decades of elections in which every race had only a single candidate, chosen by the nomenklatura).