East to west is fine. You will encounter headwinds no matter which direction you go. In the panhandle of Florida there are three good routes. One is highway ninety which is quite hilly is some stretches. You can expect sidewinds from the north which will be parried by the many stands of pine trees. South of 90 is highway 20. It too is hilly but perhaps less so than 90, and maybe less interesting and historic. Highway 98 runs you right along at the water's edge. It is mostly level the way I remember it. A downside is that stiff sidewinds off the gulf are normal daytime events, and they will slow you down. Also, the distance is longer adding perhaps an entire day to your journey. I measured the difference once off maps. I think it is about 60 miles longer than 20 or 90 because it follows the contours of the very uneven, unstraight coastline. 90 is the suggested route. I have used it a few times by bicycle. It is a very good ride. There are plenty of places to camp, free camp, and to eat and buy food. Probably 90 is your best bet. I took other routes because I was already familiar with 90. 90, 20, and 98 will get you to the same general destination for going into Alabama.
There is no all encompassing, comprehensive information on W to E versus E to W. Just go. The wind is there. You cannot escape it. It's part of long distance cycling just like rain and storms. I have done the ST several times. I went E to W. Very often it was a quarter wind from the SE that gave a push. In winter there are northwinds full of cold. Out west getting into west Texas and nearer California there are west winds that will put you off your bike for days. I have not run into those on a bike. I have been in them in a car. Those do not come regularly all the time. They happen. I am 63. My last ST run was in the winter of 2009-10. I got from near West Palm Beach, FL to San Diego in 54 days total with 43 days actually pedaling long distances over the road, and that was with deliberately holding back for two days to make sure I would get into downtown San Diego early in the day.
Don't sweat the wind. Just go.