I saw Martha Raye as Dolly one month after seeing Carol Channing on tour as Dolly. I saw Channing from the next to the last row of the balcony in a 2400 seat theatre, and saw Martha Raye from the front row of the St. James. I was familiar with Raye from TV, and she was always quite the comedic cut-up. I thought of her as "mugging" quite a lot. However, she played the role of Dolly quite legitimately, sang well, and her comic talents worked well in the hat shop scene and the eating scene.
By the time Martha Raye did the show, it was running out of steam. The producers offered deeply discounted tickets to US Servicemen. This was during the Vietnam War era, and Martha Raye was known to the troops because she often traveled on USO shows.
Betty Grable followed her for a short run. Then Pearl Bailey rejuvenated the show with a two year run.
I did not see Phyllis Diller.
Ray is the author of the Brad Frame mystery series, and two suspense novels. He is also the author of a one man play based on Ben Franklin. http://www.rayflynt.com