Also, should I consider Zoysia seeding? I don't know much about Zoysia... How would that come in if the bermuda decides to return after tilling?

Some more info after reading descriptions of bermuda strains. I have two medium sized dogs running around the back yard all the time, I'm not looking for a putting green. I've also been moving towards the mow-high, water deeply/infrequently, reel mower leave clippings method of lawn. Really trying to go organic but can't until I fix this clay soil.

Just because I'm curious, why are you going to have to remove soil to add organic matter? I can understand if you have drainage issues or other considerations which may apply but typically, adding organic matter that will eventually become part of the soil base by decay will only temporarily add "height" to your soil levels. That increased height will decrease as the amendments integrate into the clay and you will probably be left with about the same height soil level you have now after some period. Not saying adding organic matter isn't good as it's the best thing you can do but with active dogs, you're still going to get paths and foot pounded areas from your pets.
As to tilling your existing Bermuda, my experience has been that it will take something barely short of an atomic bomb to kill all of it. Yes, it will look really bad for a while but inevitably, many rhizomes "buried" by your tilling will start to grow again although it may take more than one season to recover. Reseeding will help fill in.
I think it's a misnomer to assume that when a lawn gets "old" that it needs to be redone although regular maintenance (some of which you're already planning) will help any lawn thrive despite its age.
As to the best grass strain, contact your local AG Extension service for recommendations. It's a free service provided by your taxes so why not take full advantage of free advice by experts familiar with your immediate area...
Steve

Thanks for response Steve... Now that you mention it, and I think about it, I probably won't have to relocate any soil since it will eventually settle.

Yes, I have drainage issues. The soil is simply all compacted clay. Topdressing is not helping increase organic matter. I should really call this a soil rejuvination, not "Re-Do."

I can practically guarantee you that your soil is not clay. It may act like clay, but unless you have a clay brick factory in your neighborhood, it is not clay.

I want to discourage you from rototilling with all my heart and soul. All it does is fluff the soil and leave an uneven subsurface where the tiller bucks up over a root and digs in where it's soft. After you level the top, that leaves the uneven subsurface for the fluffy soil to settle down against. When all the settling is finished, you will have an uneven surface which leaves your lawnmower scalping as it rolls into the low spots and holes. If your soil surface is uneven now, then you should level it. Search this forum for topics about leveling.

If you know the basics of soil then you know about soil structure and the billions of microbes living in the soil. And you know that there are entire species of microbes which cannot survive unless they have air contact and other species which cannot survive IF they have air contact. And that the microbes generally live off of the sugars provided by roots and off the protein provided by dead animals (other microbes, insects, or protinacious plant matter). And you would know that the beneficial fungi in the soil can send miles and miles of microscopic hyphal structures out into the soil to separate "clay" particles and allow air and moisture to penetrate deeply and give that soft feeling when the soil is moist. And you know that you can provide food to those microbes by applying something like alfalfa pellets (rabbit chow), corn meal, soybean meal, cottonseed meal, wheat flour, etc. to the soil at a rate of 20 pounds per 1,000 square feet and letting the microbes decompose it. And that by spraying the soil with something as simple as shampoo at a rate of 3 ounces per 1,000 square feet and repeating in 2 weeks you can soften the soil so it no longer has that clay-like look and feel. Well, maybe that went beyond the basics of soil care, but those sort of cover the basics of things you need to know to take it from here.

I have been using organic fertilizer (described above) since 2002. When you stop using chemical fertilizers, other issues seem to clear up. I have also stopped using compost because it's expensive, it doesn't seem to help, and it is a royal PITA to apply. I consider what I do to be a 'no hassle' approach to lawn care. It doesn't matter if I over apply organics (I cant) or if the rain comes and washes stuff away (it won't) or if I used it last week and want to use it again this week. You can't make a mistake unless you apply so much that you smother the grass (that's about 80 pounds per 1,000, by the way).

The rye grass prolongs the regrowth of bermuda in the spring. You should have a healthy stand of bermuda by the end of April but with the rye, it will shade the bermuda allowing all sorts of problems to happen.

So here's the advice part
Find the Bermuda Bible online and memorize it
Forget about rototilling - concentrate on leveling. Level it next June or July when the bermuda has recovered from the damage caused by the rye.
Spray the soil with shampoo to soften it. It should be a clear shampoo like baby shampoo.
Apply alfalfa pellets to feed the microbes. The microbes will feed your plants.