Yep, we can go with FF black mage-type of magic system.

It's a good idea to tie the element to each 'sin'; thought I should elaborate that for simplicity sake I'm also debating if for this we'll focus only on the sin of wrath, which for this case is the 'consequence of the cause'.

In the Greek view on the seven sins, they believed that pride is the root of all sins. My interpretation is that:
Pride, a sin that stems from self-importance, would expand to
Envy, unwanted obsession over things one does not possesses, to
Greed, of materialistic obsession, which escalates to
Lust, of emotional obsession, to
Gluttony, obsession to gain more than what one needs of anything, to
Sloth, depressive state when none of the above is enough to satisfy one's needs,
And lastly, wrath, hatred born from the depths of dissatisfaction and despair.

Not sure if I'm making much sense though - still not quite recovered from my fever.

'Riamancy' is a good name! Will include that in the lore.