Still, on the evening of the day London was bombed, they signed the £11.5m deal transferring four playhouses from the Really Useful Theatres group to a new company, Nimax.
On 3 October, Weitzenhoffer and Burns take ownership of the Apollo and Lyric in Shaftesbury Avenue, the Duchess in Catherine Street and the Garrick in Charing Cross Road; the four playhouses left in the RUT West End holding from the Stoll Moss Group Andrew Lloyd Webber and RUT bought in 2001. RUT retain the musical theatres, including Drury Lane and the Palladium.
"It was logical" says Burns. "But it was kind of heady in the end. We didn't know it was going to come off till we were signing." The deal puts a new producer-owner in the West End, with RUT, Delfont Mackintosh and the Ambassadors Theatre Group.
In the rumours about a sale, Weitzenhoffer emerged as a likely buyer. But when did Burns get involved? "It just sort of came up," she says. "Then there was a conversation when Max said, 'We could do this.' We both went quiet, then we said, 'OK,' and hung up."
They are equal partners. "Just me, Nic and the bank," Weitzenhoffer says. "And my husband," she adds. "I'm deeply fond of Marc [Hutchinson, a lawyer], he's deeply fond of our house, and we intend to stay living in it."
Weitzenhoffer was a bidder when Lloyd Webber bought the Stoll Moss theatres in 2000. He was also interested when the ACT theatres were sold to the Ambassadors Theatre Group, but insists he never made an offer. In 2003, he did buy the Vaudeville, now host to the long-running Stomp.
A 65-year-old Oklahoman oil heir, he fell in love with theatre and movies at the age of five. He can remember the Broadway production of The King and I with Gertrude Lawrence - "she got cancer and died during the run". His son Owen is named after the Henry Fonda character in his favourite film, Fort Apache.
It was Broadway that grabbed Weitzenhoffer, and he won a Tony for Dracula. But he's made his home here now, with his young Japanese wife and their two children, four and two, near Winchelsea.
He first worked with Andrew Lloyd Webber on the New York production of Song and Dance more than 20 years ago, "and we've worked together on financing stuff ever since". He's known Nica Burns for some 12 years and worked with her since 1999.
She was an actress who became the artistic director of the Donmar in 1983 and an independent producer from 1989 when she got involved in the Edinburgh Fringe - she is half-owner and director of the Perrier Awards. In 1993, she was taken on by Janet Holmes à Court as production director for Stoll Moss, then switched to Really Useful.
What will be the hallmark of a Nimax show? "Quality, drama," they both say, with emphasis. With an American flavour? "No, look, our record stands," Burns insists. "Together we did Feelgood, a commissioned piece from Alastair Beaton about Tony Blair and British politics. And we did Medea, Deborah Warner and Fiona Shaw. You can't get more of a fixture in British theatre than Fiona and Deborah."
They are together responsible for Some Girls, a new Neil LaBute play doing rather well at the Gielgud. Last week, it covered its costs and Burns and Weitzenhoffer took the cast out for a celebratory dinner. "It's only right, we love 'em," Weitzenhoffer says. They also did One Flew Over the Cuckoo's Nest last summer, first in Edinburgh and then the West End.
Christian Slater is being brought back to the West End by Nimax in the autumn for Tennessee Williams' Sweet Bird of Youth. "Over here, you think Arthur Miller is the greatest American playwright ever," Weitzenhoffer says. "But to me, Tennessee Williams is absolutely the one."
He and Burns found they have the same taste, he says. Neither are much into revivals, and they won't transfer other people's productions unless they're outstanding.
Yet in November they will revive a show Weitzenhoffer did on Broadway in the 1980s, Burn This, which starred John Malkovich. There was a New York revival a couple of years ago, and before Burns can stop him, Weitzenhoffer says: "That was appalling - no Nic, I can say it - because they hadn't got it. The lead has to be steamy like Malkovich was, otherwise it doesn't work". They don't yet know who the London lead will be, but he will be steamy.
Lloyd Webber said he'd only sell to theatre people. Nimax are not only theatre people; they know, and have worked with, all the major West End principals.
That means clashes will be avoided: "No Rodgers and Hart shows within a month of each other, no Arthur Millers at next-door theatres," Burns says. "The West End's mission is to provide shows for the whole audience, so there's almost something for everyone." "Yeah" says the other half of Nimax. "We're part of that."