OAT Destroyer, although I did not personally use it, is (according to almost everyone I know who has used it) more difficult than the actual OAT.
It's tough to give advice with respect to rescheduling, but remember that you can always take the OAT a second time if need be. You do, of course, have to reschedule with enough advance notice, so if you were to have any chance of that, you'd probably have to call immediately, or as soon as they open tomorrow. NMR spectroscopy isn't that important, in that yes there should be a couple questions on it, but it's a topic that isn't critical to the understanding of any other topics. Just remember the fundamental point that NMR spectroscopy differentiates between 'different' (i.e. not perfectly 'symmetrical') Hydrogen atoms, or in the case of C-13 NMR spectroscopy, between 'different' Carbon atoms. IR spectroscopy, on the other hand, differentiates between functional groups, a prominent example being hydroxyl groups vs. ketones or aldehydes.
My study advice is this: Know as many of the reagents for O-Chem as possible, know nomenclature and aromaticity, and it helps to know the official names of the more common reactions too. As for general chemistry, it sounds like you know enough that you will probably be fine, because PV=nRT, mole fractions, etc. is a sizeable chunk of that section. Make sure you can handle atomic orbitals and ions, and at that point, just take the test and do your best.
Best of luck Friday!