You used the best method for determining type.

The Si/Ne Ni/Se & Ti/Fe Te/Fi dichotomies (Decisive/Judicious - Merry/Serious) are the easiest things to type with a pretty high level of accuracy. But then again this is just my opinion on the matter.

I find the differences between the introverted and extroverted form of the same function profound(Fe/Fi for example). And odds are you're not going to end up in the wrong quadra through that method, since each quadra is a mix of certain function values, and it's consistent through the whole quadra.