I would not be using Leveler. Leveler is a brute force peak limiter and intentionally creates distortion. We are considering dropping leveler as the only use any of us have found for it is to create Air Traffic Controller voices.When I made the original recording, I was using (I can't remember the preamp, but it was USB) and kept the input gains low, the input volume low on Audacity and then all I did was use normalize and leveller after recording to get the right level of volume throughout the recording using the default settings for the normalize and leveller.
"SoCal Approach. United three six Heavy clear for landing Two Four right."
So unless you're show is the controllers at LAX, that may be creating more problems than it's solving.
You can try Effect > Compressor. That boosts low volume sounds at the expense of high volumes ones, making things louder (but bringing up the noise a little, too.) Use gently, that may solve your overall volume problems without creating harshness.
Amplify and its cousin Normalize just manage overall volume like turning up and down the volume on your radio. People find right away that they start running into peak volume damage using only those two. You can check for that with View > Show Clipping. Overload damage is shows by red stripes in the blue waves.
And if you just can't make it all fit any other way, then yes, Leveler may be for you but I'd be happier with that if you weren't complaining about harsh distortion.
And just because we've taken it this far, listen on somebody else's sound system. I got a pair of terrible headphones once and I caught it before I tried mixing anything.
Koz