No, HTML imports are the kind of technology that are the perfect architecture for this kind of web app and arguably are what make it possible. It'd take a whole blog post to explain, hopefully I can write it up soon!
I could understand if you said you need WebGL or WebAudio or some other hardware/OS interface. You don't need HTML imports.
Look, I understand how one might like HTML imports. Once you've gone down the rabbit hole of Web technology, all the fancy experimental features make it look like HTML/CSS are now adequate. They're not. It's a trap.
The real answer is writing Javascript (or something that compiles to Javascript). Always has been, always will be. Don't trust the web consortium to specify things that maybe browser vendors will implement. Do it yourself now, thank yourself later.