Hi Anna,
I have Zoysia and high quality Burmuda... love both of them.
Here is your big problem though- shade. Honestly, no other turf grasses will grow much (if at all) in shade except St. Augustine. The six hours of full sun rule applies here. If you have less, you are stuck with St. Augustine- even then, shade makes it rather weak. Dry shade (under trees) is even more difficult.
I used to grow St. Augustine but the wonderful summer of 2011 made it go bye-bye. I could not keep up with the water needs when the endless days of 100+ degree day hit.
I have seen many people in your situation (if the remaining 1/3 of your yard is small) fake it and just mulch the whole area with hardwood mulch. Yes, there are draw backs but in the end, it does look rather nice. "Mowing" consists of a couple times per season of a quick shot of Roundup.
Sorry, I know this was not much help but I would hate to see you send $ on turf that will do even worse than the St. Augustine!
