The 90-minute cycle is actually a "textbook example" that loses all applicability in real-world situations.
It's a bit of a false meme that's spread like wildfire across sleep advice websites.
The top graph is the "textbook example" I'm refering to. And those aren't even 90m cycles. Cycle length changes depending on our circadian phase (i.e. time of day). Notice how cycles in the early part of sleep are much longer than 90m.
As we age, our sleep architecture becomes much more choppy.
And it's not just age, your homeostatic and circadian sleep drives will turn those cycles into anywhere from 60m to 120m...
Take a sip of alcohol or caffeine before bed and your sleep stage architecture will become sporadic - no more 90m cycles. Too much stress (i.e. cortisol)? No more cycles.
Worse, you're doing polyphasic sleep. You'll almost never see consistent cycles. You're sleeping against your natural circadian drive. Your sleep architecture is going to be very different. The 90m rule will have no application for you.
Right now I'm looking at real data of sleep stage architecture graphs from a pdf version of Stampi's Why We Nap book. The data is from polyphasic subjects. I can't see any evidence of predictable cyclic patterns.