How to Speed up Header Image load time

I am not sure I can quite explain my question well.. on my site test4.franciscanfriars.org I am building a website with lots of pictures. I am using the maximum number of slider images, 12, and everything seems fine.. I uploaded a variety of images of different resolutions, everything looks fine and seems to load quickly... But when I started to upload several header images, and chose to randomize them, I found that they load slowly! I currently have 17 different header images that I am randomizing. They all seem to take a noticeably long time to load... I've experimented some with different number of pixels, and compression, trying to get file sizes of the images smaller... Am I going down the right road?? I know the recommended header image size is 1680 x 720. I have reduced some images to 840 x 360 and that makes the file size smaller... also I can compress the images to make the file size yet smaller, but at some point image quality suffers... is there a recommended file size (in addition to pixel size) that makes loading time reasonable?