odie dragon - it is possible to get straw that does not have weed seeds, get if from a farmer and ask them if they cut it before it went to seed or find a local farm that sells it and leave it out in the rain to see if it sprouts.

an alternative method is what organic farmers do and that is to use plastic mulch with the drip irrigation is usually run underneath it. this method works best with transplants for most things you have on your plan except for carrots and leeks and lettuce that is direct seeded. The down side it that the plastic gets thrown away at the end.

You could still use your landscape fabric, which I have used before and some weeds do come through, but you could put straw on top of that. Just make sure to pull it up at the end of the season and plant your cover crops again.

I suggest putting down compost before you do your planting/mulching too!

Good luck.