A small word of caution, from this long-time resident:
Please don't over-think the situation!
I definitely agree that a west-facing lanai is not comfortable here, no matter the season. But, folks find ways around being baked, there!
Most lots are designed to accommodate the category of homes in the immediate vicinity. Thus, an area designed for Designers will, for the most part, have lots suitable to accommodate any Designer model, BUT with little flexibility as to how your home is oriented.
My bottom line is that you'll find the lifestyle so attractive and engrossing that you won't really care all that much about your pad, because it'll become only a place to crash for the night!
SWR