Sounds like you are leaving too much space on your left side. You should really clinch tight up in there, driving your head and crushing their guts to close off all potential space underneath your arms and between their body and your neck.
I recommend working with someone, going to the old school position and having them attack the darce slowly so you can feel the gaps that they are leaving open. Then manually tighten up and close those gaps... re-drill the move this time being mindful of the space you are creating.
Hell, when I used to attack from the lockdown half I used to leave gaps so wide that wrestlers would just wrap me up into a cradle and fold me until I tapped.