Corps, I doubt that you will be DQ'd if you submit the paperwork stating your prescription (as verified by your eye doctor). If DoDMERB has already reviewed your file, it may take a little longer, but you shouldn't need a waiver. It is great that your eyes are improving since 7.87 is a little too close to 8 for comfort.
TriService, from what I know, you are right about this. However, this assumes that you don't have other eye problems, like colorblindness, lazy eye, significant astigmatism, etc., for which a waiver may be required.
By way of encouragement, the eye exam is really not as scary as many candidates think. I have rather poor vision uncorrected, but with glasses I can see 20/20 no problem, and I had zero difficulties with my exam. As long as your vision is correctable to 20/20 and you don't have eye issues, there is a very high probability that you will do just fine on your exam.
Oh, and if for some reason you run into DoDMERB problems, email Mr. Larry Mullen (the DoDMERB Deputy Director). His contact information is posted in one of the earlier DoDMERB threads. I have read his posts before and have seen others' comments about him, and Mr. Mullen is AMAZINGLY helpful. Definitely contact him if you need any help with the process.
Best of luck to both of you!