I do a number of things starting in the spring to keep my bermudagrass looking good.
1) If I have the time and the will before the bermuda comes out of dormancy, I'll spray a round-up type herbicide some years. I actually use Eraser. I know you said you didn't want to do that, but it works great. I don't like to do that every year, however.
2) Put down some kind of pre-emergent to catch some of the other weeds before they come up.
4) Fertilize. I alternate between 34-0-0 and either 10-20-10 or 13-13-13 from year to year. Be careful with the application 34-0-0 once it gets hot. Pure nitrogen can burn up the grass. I usually do another light application sometime later during the summer.
3) In the spring, before it gets hot, if I haven't already used round-up, I use 2-4-D as a post-emergent herbicide. It will kill most broadleaf weeds. If it's less than 80 or so degrees, put it on a little heavy, say 2.5 to 3 oz/gal. Once it gets hot, you can do 2 oz/gal. 2-4-D does an okay job, but may require a couple of applications 2-3 weeks apart.
4) Once it gets over about 90 deg, I ditch the 2-4-D and spray MSMA. It is a better post emergent herbicide that will kill almost anything besides the bermuda. Like the 34-0-0 fertilizer, you need to be careful once it gets really hot or it can burn up the bermuda. I find that 2 oz/gal won't hurt the bermuda in the hot part of the summer, but may "knock it back" a little. MSMA is particularly useful if you have Dallisgrass. That's about the only thing I've found that will reliably kill it.
5) I have a Nutsedge problem at my house. The ONLY thing on planet earth that will reliable kill that shiznit is a product called Sedgehammer. That's all I have to say about that.
In my opinion, and in my area which may be more fertile, you don't need to seed bermuda unless you have pretty massive gaps in it. Properly de-weeded, fertilized, and watered, that stuff will fill in holes very quickly.
Now, I live in southern Oklahoma in the Washita River bottom. We get up to 105°F regularly in the summer, but do not need to irrigate. I do typically water for a few weeks in the hottest part of the summer, but we generally stay wet enough to grow grass without it, although it may not stay really green. In the fertile valley, we have many different kinds of weeds that come out at different times throughout the year, so my methods are predicated on that fact, and is ongoing throughout the grass growing season. If you don't have all those different weeds in your area, you may get by with less herbicide applications. You'll have to figure out what weeds you have, and what will kill them effectively. The main thing is, most weeds really rob the nutrients from the bermuda. If you can get those nutrient sucking SOBs out of the way, the bermuda will kick butt.
Edit: I just read the most recent posts that popped up while I was writing. I see that you prefer no liquids. Nearly all the weed control I do involves liquids, so I guess it won't help you. I have no idea how to kill weeds without it.
