too many sharing buttons

That depends on how the plugin adds those posts. You can, however, fix things yourself by removing sharing buttons from specific areas of your theme, as explained in the first part of this post:
https://jetpack.me/2013/06/10/moving-sharing-icons/

You could for example remove sharing buttons from all sub posts thanks to is_main_query().

I hope this helps.

It turned out to be easier than that.
The developer of the Quick Ajax plugin suggested the following custom css

.ajax-item-content .sharedaddy {
	display: none;
}

which works fine. And the variant below fixed the same problem with Shortcodes Ultimate:

.su-post-excerpt .sharedaddy {
	display: none;
}