The Stubble as you call it does not go away, and using a verticutter does not make it go away. You do not want it to go away as that is what the grass blades emerge from. A Verticutter aka Power Rake is to remove thatch, or lift thatch up and break it apart so you can rake it up and remove it as seen in one of the pictures above. Thatch is nothing more than a build up of dead plant material that has not decayed and becomes compressed at the soil lever and prevents air, water, and nutrients getting into the soil and must be removed periodically. The Verticutter or Power Rake can also be used to loosen up the top 1/4 to 1/2 inch of soil to prepare for seeding or over seeding. The Stubble that you see is actually what is called Stolons from which the grass blades emerge from at the Nodes. In other words the Stolon is like a stem. When Bermuda is allowed to grow tall or cut too high and infrequently the Stolons will grow vertically rather than horizontal along the ground. It is a defense mechanism to reach up for sunlight. Mow it short. mow often, keep it short and the Stolons will then grow horizontally along the ground like you want to form a tight dense carpet of sod.

Black plastic doesn't work well for solarizing soil because it absorbs and transmits heat, instead of allowing it to pass through and trapping it. If you are determined to do this without pesticides (which, ironically, are usually far less damaging to soil microorganisms than solarization) I have used one more method (I got the idea from an everglades reclamation project) with good results: 1.) Trench the soil along all of the hardscape surfaces adjacent to your planting area. 2.) Call local Arborists and ask them do dump mulch either on the planting area itself or some place nearby and 3.) Spread the mulch to a minimum depth of 6" over the entire area (9-12" is better) 4.) Water the entire area and do nothing for about a month 5.) Plant through the mulch, being careful not to get soil on top of the mulch (dispose of any extra soil from your planting holes elsewhere on your property). 6.) Be vigilant for Kikuyu Grass (probably what you are calling "crab grass" and a weed 1000x worse than Bermudagrass ever thought of being) popping up around your new plants. I only recommend the above described method for minimally irrigated areas (I give the area a deep soaking once in the fall to jump start the growing season, occasionally irrigate during dry spells over the winter and then another deep soaking after the last of the rains in the spring - generally by the first of May). I usually mulch the area once a year, after I've done my summer pruning (which largely consists of weed-whacking the dead stalks of some of the tougher leaved South African bulbs (Watsonia and Chasmanthe are particularly annoying in that regard). Ryan

Annual crabgrass is also a guaranteed return visitor as soon as it becomes early spring again. There are no shortcuts to establishing a newly sodded lawn that will grow deeper roots/become more drought tolerant, resist weeds and grow well. Get over the idea that you can take your idea of shortcuts and it will work out well. If you do have a perennial rhizome type grass like St Augustine/Bermuda grass or Kikuyu grass, you'll be better off treating with herbicides several times before using a sod cutter to remove it. Do a search on the topic, all the best strategies pro and con have been well discussed here many times in the past.

While bermuda can be beautiful, it is a hassle to keep it looking nice. It is one of the few grasses that should be mowed at the mower's lowest setting. Partially due to that, it should be mowed twice a week during the summer to keep from scalping it every week. Bermuda also needs as much water as all the other lawns if you want it to be green. The idea that it needs less water depends on your tolerance for brown grass. When bermuda gets very dry it becomes dormant and turns brown. When St Augustine dries out completely, it dies. Thus you have to water St Aug to keep it alive but you could stop watering bermuda altogether and it would remain alive but brown. Bermuda also needs monthly doses of high nitrogen fertilizer to stay green. This is to say that you can have a bermuda lawn but if you are not willing to maintain it, it is going to look raggedy. It can also thin out and become a haven for weeds. Back in the 50s, before the modern herbicides became inexpensive, when you bought grass seed you got a mixture of a fescue, Kentucky bluegrass, rye, and even clover. The idea was that one of the grasses would dominate in almost any soil and you could have a green lawn with multiple species of plants. That approach is one you might consider. You are in the transition zone meaning that you would be able to grow almost any grass.