You might want to check out this book:  
https://www.amazon.com/Four-Season-Harvest-Organic-Vegetables-Garden/dp/1890132276
If you don't want to purchase it, you can probably get it at your local library, and if they don't have it, they can order it in for you.  He does a great job of explaining various options, as well as how to create and use micro-climates to your advantage.  You might consider a cattle panel green house, a cold frame, or even make a hay bale cold frame.  If you want winter tomatoes, I'd go with the CP green house.  Super easy to make.
IF you're going to use the weed sheeting, why bother to spray with the weed killer?  Even organic is going to have a negative impact on the soil.  You could lay down several layers of cardboard, or lots of newspaper, and then the mulch.  What will you use for soil?  Before going to this expense, do a little research on Back to Eden.