Default AOSP Keyboard vs Google Keyboard

On my Nexus which is running Google's Yakju 4.3 I have the Google keyboard as my one an only default input method. The benefit to this is I receive the updates to the keyboard even yesterdays update (blue and white color change). On a custom ROM such as CM, the default keyboard is the AOSP keyboard. Is there a way to flash the Google keyboard over the AOSP keyboard making only the Google Keyboard the only available one? I realize you can download the Google Keyboard separately from the Play Store however when this was done while running CM10.2 you cannot disable the default AOSP. Sure you can enable the Google Keyboard as well but the haptic feedback became extreme and the text input would lag. So is it possible to replace the AOSP with the Google Keyboard as it would appear on a device running a stock 4.3?
Samsung Galaxy Nexus (Maguro) | CM 11 Official Nightly 03/10
2 x Samsung Galaxy II HD LTE (SGH-I757M) | CM 10.2 Unofficial 01/20
Motorola Atrix HD LTE (MB886) | CM 11 Official Nightly 02/09