I found a green card sponor and I am in document preparation now. I don't get VisaScreen yet but already applied for it. I want to work as early as possible too. You may start your VisaScren as fast as possible no matter you start to apply for green card or not. VisaScreen may take you up to 6 months to pass it even you have everything ready.
Looking for green card sponsor or filing for green card, applying for VisaScreen meanwhile preparing for English test.
I post some info and question at www.immigrationportal.com. This website is very informative. You may have a look. Good luck.