The episode guide for my book (put together by the incomparable Brendan McLaughlin) gives a bit of a hint to how the change was handled. The last "normal" week of Password appears to be September 2-6, 1974, Joyce Bulifant and Joseph Campenella. After that, they did theme weeks for more than two months. Celebrities and Their Wives Week, then a four-star week, then Allen vs. Betty with celebrity partners, then Celebrities and Their Wives again, and then a week just listed as Joyce Bulifant and Loretta Swit (which I strongly suspect had some added wrinkle to it because it's odd that it's buried in the middle of everything else), then Carol Burnett vs. Vicki Lawrence Week with guest partners. And then two weeks themed "Winners from Past Years," which seems like a formal goodbye to the old format, and then a rerun of a previous special week.
So basically, the show's approach was that they weaned viewers off the old format for two months and then just did a total relaunch.