The "time to shodan" is actually less important than the idea that we examine it. And as I outlined, there are already lots of models in place that agree with each other. "Time to shodan" really is about 300 days of training,
Not to contribute to the thread drift but your math is off. The 300 days are from 1st Kyu. The actual requirement from day one to shodan is 1040 days. 6th Kyu 20 days, 5th 40 days, 4th 80 days, 3rd 100, 2nd 200, 1st 300, Shodan 300 days.
3x52 weeks = 156 days. 1040 / 156 = 6.666...
So you're off by roughly 4 1/2 years. More if you go by NY Aikikai standards, they require an additional 100 hours.