I would argue that "see you later" is the most common English equivalent and should also be accepted.
nope cuz the translation to this should be "أراكَ/كِ لاحقًا" "Araka/ki Laheqan".
Though one should argue using the word "God" instead of Allah. Unacceptable!
Allah could mean God, So that's fine.
So "Until next time, God willing!" is wrong, is it? Well, what a surprise!
ALLAH is a proper noun so it can't really be translated. Its a name that God has given thyself. The translation of 'The God' would be 'الرب'.
Nevertheless, ALLAH willing should be acceptable as Muslims use this phrase in the English speaking countries.
The exact translation of ان شاء الله is 'If ALLAH so desires'