Jolmes

Sorry, just reread your post. The 20 hours a week post would constitute full time work. That would indicate you have enough experience. 

My understanding is that you need a minimum of 2 years full time work experience completed after your bachelors. I'm not 100 % certain, but I would doubt you'd qualify currently.  The summer internships combined nearly equate to a year's worth of experience, so you wouldn't have much more to do. 

Would you have enough points even after gaining the work experience? Any work experience used for the skills assessment can't be used for the visa application, so you couldn't claim any points for that. The PhD might provide enough points though.