Well of course I can only comment on what I hear, and since the question was based on a difference between monitoring the sound and the rendered MP3, I cant hear that...….
You might try mixing down to wav and comparing, see if there's a clue there.
And judging based on the sound clip supplied, I am not sure about the input levels, they may not be so much a problem at this point, I don't know.
Commenting strictly on the guitar, since that seemed to be most of the point of the question and audio clip:
I would suggest at least some improvement could come from working on the Zoom device settings.
Focusing on the two primary guitar tones, both are quite "thin" and "trebly". Not much "meat" to the timbre. Especially the higher pitched arpeggiated playing. Very harsh tones.
I think I would try reducing the wet/dry mix where applicable to reduce the amount of processing, and adjust the tone knobs where applicable to get more mid/lower mid tone.
It also might help to be sure to set your tones in context and not in solo. What sounds good alone rarely sounds good blended with other sounds.
I have found in general, when it comes to guitar processing, in most cases less sounds better. Too much rarely sounds "warm" or "nice" IMO.
But as always, its hard for me to judge your intent. That may be the sound you are going for.
Hope that helps!