Instead of a minimum time frame, have a minimum number of classes. Or a minimum of time AND classes. Our syllabus states a minimum number of classes and time. My teacher looks at the number of classes, not so much at time for kyu ranks. There have been people who tested earlier because they had more than enough classes in. But they were always ready to test.
Stress it’s a MINIMUM and not a rule that they have to test after X classes and/or time.
Example:
Promotion from to 1st kyu
...(Skipping parts about all previous material, requirements, CI’s approval et al)...
“Minimum 6 months of training AND 60 classes since last promotion.”
If your current interval is 3 months, take the minimum number of classes you think they should attend per week and do the math. Make it a number they can honestly hit, given there aren’t the same number of weeks every month, dojo closings for holidays, etc. 10 classes per month sounds like a good average to me.