Soft Matzah for Ashkenazim

Question

The Rama in 460:4 writes that one should make thin matzos and the Mishna Brurah 16 writes it should be thin. Rav Nebontzol (in his notes on the Mishna Brurah) points out the Be'er Heitiv 8 which writes the custom is to make it an etzbah thick, yet Rav Nebontzol writes further that such is not our custom; he adds that Rav Shlomo Zalman Aurbach held the custom of the Ashkenazim is to make the matzah as thin as possible.

Which Ashkenazic Poskim allow the soft* type of matzah for Pesach? Even though it may fit the requirement of the Rama, does one need a special mesorah to eat the this soft type of matza?

I know many people who would not eat it on Pesach, and certainly not for the mitzvah.

_{*Definition of the soft matzah: it is around a half inch thick and is soft.}

Answer 1

Rav Herschel Schachter has written a Teshuvah that Ashkenazim may eat soft Matzah. See here* for a discussion of his Teshuvah and some follow-up questions and answers about it.

_{*Be advised that this is taken from a commercial site selling a product under the umbrella of "approved by Rav Schachter". It is, however, a real Teshuvah, and the discussion that follows there appears to be legitimate.}