I checked with our inventor on the strings detuning within zone 2. For mass marketed guitars there is production tolerance. And 10 cents throughout all of Zone 2 (which is 3-6 turns using the tuning peg) is still within the production tolerance. A guitar string at most detunes about 1/8th of a turn during a day of hard play. You should test how much the tone changes with 1/8th of a turn even a quarter turn, which is all that you will ever see in real life. Like you said the guitar stays in tune like it's supposed to after it has been set up. Be sure to use a reliable and accurate tuner when checking, as it might have just been the tuning needle jumping from the tuning peg being turned fast and then resettling. As I said in my earlier post this can be perfected by varying the height of the footplate by moving the footplate deeper into the guitar if the note is trending down as the saddle is falling back away from the nut, and less deep if the note is trending up as the saddle is falling back.
Additionally, when discussing EverTune's ability to hold tune, with new strings the tune can change by 5-10 cents in the first weeks due, it seems to oxidation. Oxidation, also known as rust, is when Iron becomes Iron Oxide, sucking oxygen from the air and increasing it's mass. When it's mass increases by 1% the pitch drops by 5-10 cents. This will happen over days though, so if you check the tune before each session, the guitar is perfectly fine for hours and hours and hours. Also this detuning happens less and more slowly on coated strings because they are coated. It also stops after a while on any string because once the strings surface is fully oxidized, this layer protects the rest of the string from oxidation.
In terms of the palm muting, you're probably pushing down on the back of the saddles somehow. Since the saddles are floating, any force on the back of them will rock them back, stretching the strings tighter and making them go sharp. I just tried it out again myself, it's not possible to pull any strings out of tune even slightly with applying as much force as I can using the palm of my hand while muting the strings, placing my hand at or near the front of the saddles.
I hope the additional info provided clears things up.