Here's a suggestion to modify the way skills are learned. It provides a mechanism for incorporating shrines into the skill learning process, and also suggests a way to queue skills to be learned.
Each skill is associated with one primary and two non-primary giants. In order to learn a skill there is no interaction whatsoever with the giants involved (unless you want to speed up learning).
My proposal is that in order to queue a skill for learning, a glitch would have to visit a shrine for one of the giants involved with that particular skill to request to learn it. The request could still be made through interaction with the magic rock, and perhaps the magic rock would suggest a suitable tithe in order to learn a skill, maybe in the form of a quest.
Also, if that sort of thing were implemented, optionally we could queue a second skill in advance so that when the first finished, learning of the second could begin.
As an even more advanced option, what if the giants only offer the most basic skills at first? Only through devotion of worshipers (i.e. completing a worship project) could giants be convinced to start allowing glitches to learn higher levels of skills. So, for example, Humbaba might offer Animal Kinship I to start. But in order for anyone to be able to start learning AK II, we as a group would have to tithe a total of 500 butterfly milk to Humbaba. That would unlock AK II at all of Humbaba's shrines for any glitch to queue it (assuming they meet the pre-reqs).