"When I turned the switch on, I had a blue belt on the defensive. Strength training is quite necessary for being a good grappler."
no offense, but you are not really speaking from experience here if your statement is based on the fact that you had a blue belt on the run. a blue belt is a beginner with basic technique. strength plays a much bigger role at the beginning levels of bjj than it does higher up the ladder.
from my experience, and i have been training bjj on and off for about 8 years, strength training outside of bjj class is not necessary until you get to the elite levels of competition(for example, mundials, abu dhabi, etc.) where technique has reached the end of the bell curve, and even then it must be secondary to skills training. just look at marcelo garcia...hands down the best grappler in the world and he doesnt strength train. i have taken classes with him and he does a LOT of conditioning/calisthenics/partner drills/etc, but he isnt lifting weights. the guy is just on the mats training like a beast nonstop. that is why he is so good. of course some guys need to lift because their specific styles are based on different attributes, but even then it must come second to specific bjj training.
the more time you spend on the mats, the faster you will progress. if your focus is to improve in bjj, the biggest mistake you could make would be to sacrifice bjj class time for training on your own. i began training in college with a friend at the same time...i got hooked and would be on the mats 6 days a week, sometimes twice a day. he came in 2-3x/week, and worked out on his own during the rest of the week. he was strong...i distinctly remember him coming home happy one day because he had clean and strict pressed 195. anyways, he was hell for all the other white belts and tough on some newer blues, but i progressed MUCH faster than him...i was promoted to purple a few weeks before he even made it to blue.