Every time you publish a new page, you could also publish a new post that had a brief description of what was on the new page. For instance a post that said,
"See my new article on bikeriding on the Sports page"
ideally with a link to the article in the post. Then, all your blog subscribers will get the new post, and it will have a link to your new content in it.
It's a little extra work for you to make a tiny post with a link for each article you post, but the WP machinery will do the sending the way you want.
It will put all these posts on your home page, but that's not so bad. If you use the "Aside" format instead of the "Standard" format for the post, they won't be very obtrusive.