This channel, Peterson Grappling, Ivan Vasilchuk, some JJJ and Catch wrestling tutorials are bringing a more complete view of grappling and self defence. I do Shinkiokushin, but sometimes cross training BJJ and wrestling. Just recently learnt that karate has lots of good wrestling techniques 😅 (hidden like in Capoeira)
Or, after he pulls his left leg back from the fake, you can hop to the left with your right foot as you snap him down, and foot sweep his right foot w/ your left. The hop to the left puts your left foot in range for sweep, and combo w/ the neck snap puts him off balance.
Its better to throw the olympic or your firemans carry if you already jacked him up. I never tried going for a front headlock because they always gave it to me when I sprawled. you dont know how to wrestle just because you do jew jitsu.