FakerMaven:, Which Rishonim are you referring to? Reb Chaim shlita in his teshuvas does not understand any of the “Rishonim” the way you do, and neither did the Chazon Ish.
As an aside, there are much more important issues to be careful about with this mitzvah.
For example, what size is your beged? Is it at least an amah according to at least Reb Moshe’s shiur? Do you even know the shiur?
How about menufatz lishma which Shulchan Aruch says you should be makpid on. Do they even make “tecehiles” which is menufatz lishma?