In IOS8 Safari there is a new bug with position fixed.
If you focus a textarea that is in a fixed panel, safari will scroll you to the bottom of the page.
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Much like Mark Ryan Sallee suggested, I found that dynamically changing the height and overflow of my background element is the key - this gives Safari nothing to scroll to.
So after the modal's opening animation finishes, change the background's styling:
$('body > #your-background-element').css({
'overflow': 'hidden',
'height': 0
});
When you close the modal change it back:
$('body > #your-background-element').css({
'overflow': 'auto',
'height': 'auto'
});
While other answers are useful in simpler contexts, my DOM was too complicated (thanks SharePoint) to use the absolute/fixed position swap.