You appear to be conflating Scrum with Agile, avoiding doing any Scrum-like practices and avoided the clear communication problems within your team ("I strongly suspected half of the team didn't know the details of what the other half is working on").

And then you say your Agile experiment didn't work.

the sprint model of Agile easily lends itself to arbitrary deadlines and building for the "demo" of the story/epic of that sprint

"Sprints" isn't Agile, it's Scrum (See for example Kanban).

and build-up of tech-debt (e.g., build a demo for one sprint, spent next 3 sprints fixing bugs for the features of the first sprint).

That is the complete opposite of anything that any kind of agile process would recommend.

To be honest, given that you don't know the difference between Scrum and Agile I think it's fair to say you don't know what you are talking about.

I'm no fan of pure Scrum. I think it's an overly ceremonial approach to building software and the ceremonial aspects of it lead to a cargo-cult like mindset, where people concentrate on the process rather than the reasons why things are done.

But Agile as a general approach works well, and a properly run Scrum process isn't a bad place to start.