**Neither a teacher nor a native speaker.**
My favorite dictionary (dict.cc) says stricter exists.
I don't see a reason why more strict should be better or even correct.
It's a (not an ) one-syllable word.
[Strict] - [Strict-er] - [Strict-est]
[Diffi-cult] - more difficult - most difficult.
I'm sorry if I confused this grammar rule, but I thought that was the important factor (if to use more/most or not.)
P.S: Welcome to UsingEnglish