PhD supervisor will not read draft
This sounds like a case of your supervisor being too busy and pushing work they consider less essential to the background. I'd suggest that, since you have alternate sources of feedback here, that you explore those and just push on toward the end. 

I think it would be harder to avoid something you represent as a "complete" draft or a "final" draft. At that point I hope the supervisor moves your work up to the first level of importance. 

Even feedback from a third party might be valuable if you can find a way to get it. 

But there is no reason for you to stall your own progress. But trying to force someone to do something they don't see as essential in the moment doesn't sound like a plan for success. Especially when they have the power.