Bosko
It is a bit complicated about US visas. I try saying something and hope that can help you.
First I want to point out the difference between our cases. You went to US after you filed for H1B, while I stay in Canada all the time. I do not enter US after filing H1B.
1. With the approval H1B,earlest time you can legally work is OCT 1st
2. Yes, you need to come to US consulate in Toronto to get the H1B visa before starting work, since I-979 is not visa (Thanks due to XDJMs here)
One US friend says you can apply SSN 10 days after you enter US with H1B visa, because they want to check your legal status in State.
Do not worry about the project, if you are good, they do not mind your missing just one because there are going to be a lot of projects waiting for you!
Good luck!