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If its been 7 months since your last wax job then there is no wax to cut thru. Carnaubas rarely last past 12-18 weeks and most are gone in 6-10 weeks. So unless you were using a really tough polymer sealant, wax was not a factor in your polishing.
The problem is that the polishes you are using are too mild. When polishing by hand you need a more aggressive product than if polishing by machine. That's because the product needs to do a lot more work since your hands can only do so much. The IHG has no polishing/cleaning ability at all. Glazes are comprised of fillers and oils mostly and are designed to fill in light swirls and leave a nice shine. Think of glazes like makeup. SMR's are the next step up the ladder from glazes but they too are mild by design. SMR's work much better by machine.
You need something with more bite. Sticking with the 3M line you could go to Perfect-It II Rubbing Compound which should do the trick, followed by the SMR which should polish out the light swirls caused by the compound. Skip the glaze if you want to and go right to wax. Frankly, I think glaze is a waste on white because white hides the microswirls that glaze fills. On black glaze is critical to get a perfect finish but not on white.
Hope all this helps. Let us know if you have more questions.