Honestly, the time for the relic grind has past, as is most of the BiS gear grinds. These will all become irrelevant in a month with the new expansion, so you will be replacing them anyways.

Although Yoshi-P HAS said that owners of zeta relics will have a shortcut in the new relic weapon quest, the amount of effort that will be required to get your relic from zenith to zeta, or even from Novus to zeta, will likely far exceed the sum of both the time spent with the zeta before it expires, and the shortcut that will be received.

The best thing to do before heavensward, is to level as many classes as possible to 50, and get a sizeable sum of gil ready so that you can jump right into heavensward without any fetters attached. That is, if you have already finished the main story. if not, FINISH THE MAIN STORY, NAO!