Mr. Ebert wasn’t talking about dressing like women. A couple of the actors had for other roles, and none were fazed by the idea. The challenge in “Casa Valentina” is to create authentic portraits of the complicated men under the makeup. The boot camp was only a start. Mr. Page’s character, for instance, a court stenographer named George, arrives at the resort in a suit and tie and plants a kiss on his wife, Rita (played by Mare Winningham), and then asks whether she has combed out the wig for his femme persona, Valentina, which he will soon become.

For the play to succeed, Mr. Page said, conversations like these need to come across as unremarkable — normal — to audiences, and George’s heterosexuality can never be in doubt. (Most cross-dressers are straight, and sexuality is a key theme. The play, which opens on April 23, was developed by a team of commercial producers but is being mounted by the nonprofit Manhattan Theater Club.)

To make such scenes feel genuine, Mr. Page and the other actors relied on one another for confidence as they experimented — sometimes successfully, sometimes not — with their voices and body language. In doing so, the cast members, most of whom were not friends before rehearsals began, became their own sort of sisterhood.

“Something that really helped me become George-slash-Valentina was going down to the deli with Gabe and ordering lunch in my dress,” Mr. Page said during the group interview with the men in the cast. (In addition to Ms. Winningham, Lisa Emery has a small but crucial role.)

“I grew more comfortable using my normal voice to say something like, ‘Can you give me a half-pound of roast beef?’ because I found that nobody cared,” said Mr. Page, who has one of the deepest voices on Broadway — and who tried a higher, more feminine pitch before deciding it sounded arch. “At the deli, I knew I was a guy, but I felt like a girl. People opened the door for me. Gabe was way more polite to me than when I’m dressed as a man. I didn’t feel horrible about my voice. Now, I realize this is New York City, where many kinds of people are accepted. But still, I felt safe, and I felt free.”

Or, as one character in the play says of the Catskills resort, “Here, we breathe.”

Such was the appeal of the real-life resort, originally called the Chevalier d’Eon — named after a legendary 18th-century cross-dresser and spy — and then Casa Susanna after one of its proprietors, otherwise known as Tito Valenti. (It is called Casa Valentina in the play.)