The rule about the defense leaving the field of play removing the right of appeal is INTENDED to be applied at the end of an inning / game, but this is not the end of the inning. But, the rule does not actually SAY end of the inning / game (ASA), so a literal application could nullify some of the potential craziness!
Regarding touching bases, we can only rule on what players actually DO, not what they intended to do. We don't recognize accidental appeals, because an appeal (by rule) must be properly made, however, we do recognize accidental base touches for any other purpose by either the defense or offense.
In the case of the runner touching 3rd, I don't see how you could "correctly" ignore that; but the chances are, the defense won't be smart enough to appeal it.
With touching home, youngump, are you suggesting ignoring the touch of home to make life easier on the umpire?
This play is already a cluster f---, so you may as well be correct!