One way I’ve been experimenting with this is by replacing Adsense ads with my own “self generated” ads. For example, the 728×90 ad at the very top and the 300×250 ad at the top right are both simply images that link to an external page within Amazon. And on Amazon, since I’m an “Amazon Associate”, I’m in essence running ads that generate revenue for Tablet Crunch. And since these are technically only images that link to an external site (via an affiliate link), I get the benefit of having the ads render in Instagram.
So have you noticed Adsense not rendering in Instagram?