Probably not the issue (whatever is causing the long First Byte Time is) but something that will give a speed boost is running your woocommerce images through Prizm Images:
http://www.prizmimage.com/
could save over 500kb on your shop page:
http://www.webpagetest.org/result/140916_7H_66J/1/performance_optimization/#compress_images
You could also hire a specialist in wpengine speed optimization, we used this guy:
http://www.markdescande.com/speed-up-wp-engine/
