No, I don’t know of any way to remove the echo/reverb in your recording.
Echoes are very difficult. Echoes are your voice bouncing from walls and arriving at the microphone slightly later than the main voice or performance. The sample sounds like it was made in a hall or other large room, but any room with hard, shiny walls like a bathroom or kitchen will do it.
The job is removing the voice from itself. There is no “noise.”
Look for a simple, clean echo in the dialog. I chose 7.65 seconds to 8.25 seconds. Ideally, the performer would clap once just before speaking. You may have seen some musical performers do that. They’re doing it for sound sync, but that’s not the only thing it’s handy for.
Effect > Noise Reduction > Profile.
Then select the whole file and Effect > Noise Reduction: 15, 6, 6 > OK.
It won’t get rid of the echoes, but it will suppress the “thick, full, fuzzy, cottony” sound. It will also get rid of a bunch of the background hisss.