Default [Q] Is there an app to replace the Android Exchange Active Sync service?

I configured a new account to sync my work email and calendar. This results in me being able to use the stock email app, as email syncs fine, but only some calendar entries are synced. I've tried clearing the cache/data, deleting and setting up the account again, to no avail.

If I use a mail client like Touchdown or Nine, that apparently have their own EAS sync engines, then the calendar does sync fully.

What I'm looking for is an app that just provides the EAS service, that would allow me to use the stock email and calendar apps, but I can only find those mentioned above that also have email clients (and calendar for Touchdown) integrated with them.

I'm on a rooted Nexus 4.4.2