Thanks, TalismanRich! I record to SD card in Zoom H6 and then use Adobe Audition CC to process the file. I usually use the DeNoise option, and with 10-20% I will get the noise removed. If I use more than 20%, the voice get slightly distorted.Any preamp will generate noise, especially when it is cranked up. That's one reason that dynamic mikes like the SM7B and SM57/58 don't always work well. They put out very low signal levels.
You haven't mentioned anything about the software that you are using. There is noise reduction available in most DAW packages, some better than others. I processed this in Reaper using the REAFir plug-in. Does this sound quieter to you? Its your TR2 Wave file from above.
In your sample, I cannot hear any noise, but the voice also sounds differently, less natural.