Wow, looks just like my front yard. It's funny that you said you got a quote for leveling a couple years ago and it was $1200. Me too (I'm in Acworth)! But this year, that same company (LL) did it for just under $800. A result of the poor economy no doubt.
You lawn looks pretty typical for just coming out of dormancy. Have you ever read the Bermuda Bible...you should. Did you use any Pre-M?
Get a soil test before adding lime, need to know the pH (www.loganlabs.com
Did you burn it this year? I didn't realize that was legal anymore. I scalp it and bag the clippings (2 weeks ago). That's the only time I bag, always mulch. You can hit it with 2,4,d (weed-b-gone max) now to kill the broad leaf weeds. The grassy weeds may need to be pulled or something stronger like Celsius. Both houses on each side are vacant, so I have a bad bought of Dallisgrass I'm dealing with despite using Pre-M (Amaze).
For the slope I have, I end up patching it every year with sod. Bermuda is cheap!
DO NOT over-seed hybrid Bermuda with common Bermuda (Princes 77). Once you start using the right cultural practices ( Lesco 39-0-0 every 30 days), mulch cutting 2-3 times a week (as low as you can w/o scalping) water 1 "/week (roughly speaking) it will look like it did before.
I tried to upload some pics, but the site just gives me an error message.