Voltage (potential difference) follows Kirchhoff's Rules, EMF does not.
I think you've got the physics right, but I'd like to expand on this and
suggest a slight shift in terminology.
1) I avoid the term EMF. The quantity that is usually measured by
"electromotive force" is not a force at all, but has dimentinos of energy
per unit charge.
2) I use the word voltage to include induced voltages. I believe this is
consistent with usage throughout the scientific and industrial community.
3) The term "potential difference" is acceptable when talking about DC
circuits and capacitors, but when talking about induced voltages it is
crucial to keep in mind that the induced voltage is *not* a potential!
4) Kirchhoff's rules are equivalent to saying that there are no electric
fields except inside capacitors, and no magnetic fields except inside
inductors.
If you've got a circuit with an induced voltage on it due to unshielded
time-varying magnetic fields, you've got a blatant violation of Kirchhoff's
rules, but it's not because there's anything special about non-potential
voltages. You could get an equally blatant violation using potential
voltages, if you have induced currents due to unshielded time-varying
electrical fields running around your circuit.