Modifying Commerce line items after order is complete
I found a solution (possibly temporary) to my problem. Instead of trying to modify the line items via the order itself, I am modifying them directly. 

After changing the line item during the for loop, I pass the $item variable back into this code:

craft()-&gt;commerce_lineItems-&gt;saveLineItem($item);

I'm not entirely sure what the extra impact that is on the number of queries, but considering that most people will only order a single gift card, maybe two, I would imagine that it's not a terrible way to accomplish this. 

I'm still open to ideas of a better way to solve my issue, but for now it seems to do the trick.