The solution to this is to design for the iPad mini. If you make the user interface elements large enough to tap on a mini, they will also be large enough to tap on a full sized iPad. This also has the benefit of presenting a single user experience no matter what size iPad the user has, which I think is a plus.
Follow Apple's human interface guidelines and you'll get this for free. Don't treat them as sacred tomes, but it's no accident that the DPI on the iPad Mini is the same as that of the non-retina iPhone/iPod Touch, and they suggest the same minimum tap target size on both platforms.
The only exception to this is if you're making a ruler, and you're not.
I agree with you. But I think the argument against this is that the elements will be slightly larger than they need to be on the full size iPad and you are thus not making the most of the available space.