I don't know 13th Age much but I like what I've read of Icons. It seems to make the heavens a dynamic situation full of needy intervening gods.
Hack-wise, relationship points could be roll modifiers for a variant of Open Your Brain or similar. 1-point relationship could mean roll+1, or roll=0 if the base for the move was roll-1.
Or:
Petition
When you cry out loudly for a god's favour or intervention, choose a number of the following up to your mana with this god.
- You maintain your relationship with this god.
- You maintain your relationship with other gods.
- You keep your self-respect.
- You need make no great sacrifice.
Reflect your choices in how you describe your petition. The GM will then tell you if this god finds your petition favourable, your cause worthy and your need great enough. If so, you get what you want.
For Petition, player characters might start with 3 Mana to distribute among 2 or 3 gods. Unless they were the Cleric or the Paladin, where they'd could load all the Mana onto one god. And then maybe 1 mana per level or maybe mana as a boon granted for services rendered.
I can also imagine objects that grant mana for use in a petition.