There is no such thing a Saint Augustine seed. Saint Augustine and Bermuda grass do not play well together as they have completely different maintenance requirements. In the sunny areas the Bermuda is going to win out, and in the Shady areas the SA will take over.

My advice since you have shady area is have a contractor install SA sod over the area, or you can try to do it yourself, but I will warn you it is very hard to get rid of Bermuda once it is established.

Yes, but...you can. I see it in San Antonio all the time. The ONLY secret is to keep the St Augustine watered once a week (very deeply if possible). The secondary secret to allow full coverage for St Aug is to mow at your mower's highest settinng. In those circumstances, in San Antonio, St Aug wins out every time. But if you stop watering for a couple weeks then suddenly the entire area will be bermuda. I have done this myself and gone back and forth. My driveway in the back is stone. The St Aug escaped into it years ago and the bermuda volunteered. We never water the area except for my experiments with shifting back and forth from one grass to the other. In my absence and a drought year, the St Aug is all gone now. Oh and I always forget about the load of dirt the city used to backfill a repair on my water meter. It grew nutgrass and bermuda, but the St Aug filled back in. I did nothing and now it is all St Aug.

Here's the problem in a nutshell. When there is a drought, if you don't water bermuda, it goes dormant and will return at the first sign of moisture. If you don't water St Augustine, it goes dead and will not return, period. So if you have an unirrigated and mixed lawn, the bermuda will win. But at the same time, bermuda cannot tolerate any shade. That's why you have areas of St Aug now. They are in the shade of something (fence, building, tree, etc.). Since bermuda is so sun loving, anything you can do to shade it will give the edge to the St Augustine. Mowing the grass at the highest setting will provide enough shade from the St Augustine to choke out the bermuda.

St Augustine will spread 10 feet in all directions in one season. A few strategically placed flats (about $1 each at most SA nurseries) should give you a full St Aug lawn by October.

If you are going to get on an organic program, now is a good time to start with fertilizer. If you are on a chemical program, do not fertilize until after you mow real grass (not weeds) for the second time. Waiting like that ensures you are putting fertilizer on active grass roots and not just weed roots.

My lawn could not be easier to care for. I changed to organic in 2002 and life got real easy. All I have to do is water deeply once a week, mow high (as high as my wife will let me), and fertilize on the federal holidays. I only get weeds in the back where the dog and kids live. There is a FAQ on organic lawn care over on the Organic Gardening forum. It describes an inexpensive, clean, and very effective program.