It would not make much difference. The ocean is interrupted by land and the bulge can’t just travel around the planet like the common illustration shows. It runs into the land and then what? Note that the tide is not a simple clock at all but takes a complex formula to predict.
The tides are formed by multiple gyres of water sloshing around the oceans, like trying to walk with a cakepan filled with water. It has a natural period and is pumped by the actual tidal force, like a kid's swing toy is pushed once per cycle or pumped by the kid's slight shift in center of gravity.
Making the moon go pole to pole would not change that: the oceans would contain bulges that slosh around and can’t get out, and would develop a pattern of being “pumped” by the daily tidal forces. The details would be different, but I’ll bet the same formulas would apply, just with different parameters measured.
Ah, a difference is that the daily force would shift, and when at right angles would not be affecting that gyre hardly at all. So it will add a monthy intensity cycle, and increase the complexity of the formula at any particular harbor.