I think we're talking one million crossovers, easy!
Archibald Beechcroft's transformation of Toobworld's population only had an effect within the reality of the TV Universe. Just because a TV show was in production at that time, this doesn't mean their characters were transformed. Westerns were big back in those days, but their characters were long dead by 1961. So Matt Dillon and the Cartwrights never looked like Beechcroft. (The exception to that? Dr. Miguelito Loveless. It's our contention that he was alive in Toobworld until at least 1973.)
If a show took place in the future and was being broadcast at that time - let's say an episode of 'One Step Beyond' - their characters didn't become "beechcroftian" unless they were already born by May 12, 1961.
TV shows that weren't even on the air yet, though, would also have been affected by the transformation, so long as their characters were alive during that time.
Young John Locke of 'Lost' would have been transformed.
Captain Jack Harkness of 'Torchwood' would have undergone the transformation.
Mary Richards of 'The Mary Tyler Moore Show'
Fred 'Sanford and Son' Lamont.
Both halves of 'The Odd Couple', Felix Unger and Oscar Madison
Sabrina, Jill, and Kelly, collectively known as 'Charlie's Angels'
All but one of 'The Brady Bunch' kids, even as babies, would have looked like Archibald Beechcroft. The lone exception would have been Cindy - the youngest one in curls wasn't born until three months later.
Even if the TV characters were clear across the globe, they would not be spared "beechcroftization". Captain Adam Troy of 'Adventures in Paradise' would have sailed the Seven Seas looking like Beechcroft. Dr. Marsh 'Daktari' Tracy of the Wameru Study Center for Animal Behavior in Africa would have suffered the same fate. Basil and Sybil Fawlty, and all the employees and guests at 'Fawlty Towers' would have looked the same on that one day. (Polly and Manuel most likely weren't working there yet, but wherever they were in the world, they looked like Beechcroft.)
Just about the only major TV character around at the time who wasn't transformed into Archibald Beechcroft would have been Lassie!
So here's to you, Mr. Beechcroft. Luckily for the Toobworld Dynamic, you didn't learn your lesson until after you remade Earth Prime-Time in your own image. And in doing so, you may have proven yourself to be the greatest crossover link of all time!
(I was originally going to save this tribute for next year, when the whole Toobworld concept celebrates its tenth anniversary. However, who knows what may happen before then.......)