Andrew my advice would be to use Round-up since it is very efficient, safe and inexpensive. I assume your grass weed is Bermuda grass, Cynodon dactylon, but of course it may be something else. Round-up will still work.
Let your weeds grow so that there is a good canopy. This will include annuals and perennial weeds. Spray Round-up , I think the rate is 1.4% for perennials in a high volume of water to ensure good wetting. Allow the product to work, at least 3 to 4 weeks and wait for another flush of weeds.Do not disturb the soil as this will only make a seed bed for more annuals. Again wait as long as practical and allow any remnants of grasses to grow away. Spray again.
The downside to this practice will be a baked hard soil since we are probably talking up to 12 weeks which will take you almost to the autumn rains, Can you wait this long, if not try your other methods which will not very efficacious.
Of course you can forgo the follow-up treatment and get planting that much earlier.
In general try to cut down on cultivations. They produce seed beeds and weeds, destroy soil structure which leads to soil erosion and so forth. I know plants "look" better after hoeing but I think this is an optical illusion. david