Chacham: You left out the Igros Moshe and the Shevet Haleive as well (I don’t know the Simanim offhand, but the IG”M might be O.C. 1:157).
However, there is a difference between the Shevet Haleivi’s Shittah and the others (well, I’m not familiar with the Ashrei Ha’ish so I can’t say anything on that). Those other Poskim all hold that there is a qualitative difference between a capella and instrumental music. They just happen to hold that both are Assur during Sefira. (Of course, both the TZ”E and the IG”M hold that as an outcome of the fact that they hold instrumental music is Assur all year round, so you need to raise it a level for Sefirah. If your Minhag is to not Assur music during the year, then it would make sense that a capella is allowed during Sefirah.) The Shevet Haleivi, on the other hand, holds that a capella should be Muttar during Sefirah, but he holds that any a capella made professionally should be treated like instrumental music.