If you want a cheap, easy way out, start with what you have - bermuda mix. Tearing it out and starting over is definitely not the cheapest way out. If you want to have all bermuda eventually, I would focus on taking great care of it. Here are some ideas for you.
1. Spray compost tea to get a healthy dose of microbes on the soil and plants. Go over to the compost forum to find out all about compost tea. The first batch will cost you $20 for equipment but from then on, the rest cost you under a dollar to cover an acre. Compost tea is much cheaper than compost. The cost for the proper amount of compost for your lawn would be on the order of $90 plus delivery, so the tea is the ticket. You can reapply tea as often as you want to make it. It works wonders for the soil and the plants. Get a bag of compost anywhere for a buck or two.
2. Get some whole ground corn meal and spread it on the turf area. Corn meal is an organic fertilizer that will work with the compost tea to soften your soil and turn it black with organic matter. Your soil will take on a new life. The application rate is 10-20 pounds per 1,000 square feet of area. Get corn meal in 50 pound bags at a feed store for $5. If you can't find corn meal, use alfalfa meal or pellets at the same rate. Water after you apply to keep the birds from eating it all. It takes about 3 weeks to see any fertilization effect, but it will last for the rest of the season.
3. Set your mower at 1/2" to 1" in height and mow weekly. If you think you will hit rocks and dirt the first time, then rent a mower and mow it low. The reason for the low mowing is that bermuda loves to be kept low. It will 'densify' and soften quite a bit when mowed short. It will get straggly, weedy, and spikey when left to grow long.
4. Don't water unless the grass needs it. You might have to learn the tell tale signs of water stressed grass during this process. Shoot for watering no more often than once per week during the heat of summer. You may have to water longer, but the turf will be much better off for it.
Notice that I've ignored the dallis grass completely. There is a reason for that. Quite often, when we remove the focus on the weeds and concentrate on growing great grass, the weeds go away by themselves. After you've done all this for the summer, reevaluate your dallis grass situation in early September. See if you have less or more. Hopefully the dense bermuda, infrequent watering, and low mowing will discourage the dallis to death. In any case, you should have a much better looking turf and hopefully something fully acceptable to you.
Things to stay away from: fungicide, herbicide, pesticide, tillers, frequent watering. If you think you need any of these things, write back before you do it.
Please let us know what you do and what happens.
Dirt Doctor Lawns Forum