I need help using FCP subclips in Soundtrack Pro

I'm having a hard time reducing noise in some clips I'm using in FCP.

For my project, I log and capture entire tapes, import the whole tape as one long clip, and then make subclips of the bits I like. Typically, I remove subclip limits when I later play with them.

I want to reduce noise in some of them. When I send it to Soundtrack Pro as a audio project, Soundtrack Pro seems to take the entire tape that the subclip is a part of. It lets me edit the bit, but it means the Soundtrack Pro files are humongous - since it's the entire tape - and it takes forever as actions, like saving, require rendering the entire tape. It's insanely frustrating.

There must be a way to send just the audio from the clips I actually use in my timeline. No?

Please help. I'm at wits end.