For Amshinover...

A while ago Amishnover came over for lunch. Since Jameel was also there, as well as a forth chap, we had a Zimun for bentching. As is my minhag, I asked the fellow who was doing the Zimun to please say the first bracha out loud and have in mind to be motzi me on that bracha. Amshi wondered where that came from and I said it was Minhag HaGra, who held that Zimun was a Din D'orraisa (as is clear from the Gemara Brachos מ"ה) and that one isn't yotzei that unless all those answering listen to the bracha quietly and answer Amen (see Tosefes Ma'aseh Rav כ"ד). Well, that wasn't enough for him, so I'm off looking. Meanwhile, I found, in Ma'aseh Rav HaShalem:
כ"ב ר"ח מואלאז'ין דלברהמ"ז נוטל בעה"ב רשות וברכה ראשונה מברהמ"ז אומר המרך לבד.(הנהגות ישרות ס"ק קס"ג)

I'm not sure that's enough for him, but I'm trying here. I also was told that in Yeshivas Torah Temimah in Brooklyn, that is how they are noheg l'mayseh. In addition, after a quick talk with my Rav on the topic, he told me it is based on Rashi's shitah in Brachos. When I find the appropriate Rashi, I will be happy to share.