I went ahead and downloaded your map. It's not that big (about 4k x 3k). I was able to get it under 4.77 MB by reducing the JPG quality to 8, which doesn't lose enough for me to notice the difference. If you really want folks to review and make judgments on your work, you should do that.

I'm not a big proponent of the hex-style maps, although Lord knows I've played on enough of them, but others here are and it is their opinion that you'll be needing. If you need any help with the shrinkage, let me know.