I asked myself if Reinin dichotomies might be useful to determine complete subtypes. The answer to that is yes...
I also asked myself if the fact that many people consider the Reinin dichotomies useless has something to do with complete subtype theory. The answer to that is yes...
Every type has 7 of 15 dichotomies in common with every other type (except for identicals). So your subtype will probably have only 7 dichotomies in common with your base type (if your base type and subtype are not identical). That means, for most people it should be easy to determine a Reinin trait in only 7 cases and hard in 8 cases. That's why so many consider them useless...
Example:
I'm an INTj-INFp. The 7 traits INTj and INFp have in common are:
introverted, intuitive, farsighted, emotivist, merry, result, asking
So an INTj-INFp should relate most to those 7 traits and might have problems with the 8 others...
How to dermine your complete subtype:
(It can only work if you are sure about your base type and have a good understanding of the Reinin dichotomies.)
Determine the 7 traits you relate most to. If you can't do that your subtype might be the same as your base type. If your choice is correct you should know your subtype then. If you get an inconsistent result like introverted*intuitive*obstinate*emotivist*...* you either made a mistake or your subtype is the same as your base type (because only an INTj is introverted, intuitive, obstinate and emotivist).