Sounds like you should have already done this. Without going into a friggen classroom lecture on this, the herbicides that will work quickly are systemic, meaning you spray them on the plant, the plant absorbs it through the leaves and anything else it touches, and it moves throughout the plant, killing all the way down through the roots.
What are you putting a tarp and rock down for?
Anyone who tells you (and any landscaper who actively attempts to sell you) landscape fabric should be thrown on a fire ant hill and tied down.
Landscape fabric will ONLY - READ THAT CAREFULLY - O-N-L-Y - ONLY stop weeds from growing if they ALREADY EXIST in the area where you are going to throw the landscape fabric down (which can also be accomplished by throwing several layers of newspaper down and covering them with rocks so it doesn't blow away, plus it will decompose into the ground). It WILL NOT EVER NEVER EVER NEVER EVER keep new weeds from growing in that area, as the weeds will simply root OVER the landscape fabric.
Add to this the annoyance of someone wanting to run a tiller in that area later to amend the beds and getting the tines caught in the fabric, the fact that you have to cut a friggen hole ANYWAY any time you want to add more plants, and the cost of such a crappy weed "control" product, and you'd be a certified helmet-wearing tool to WANT to throw down landscape fabric. There's just no dang good reason to use that crap other than misninformation and recommendations from people who make a living at selling/installing that crap.