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"We've all heard the phrase, a picture is worth a
thousand words."

It looks more like a sentence, but maybe in loose style you can get away with . The standard setting of the whole statement, as per the Chicago Manual of Style, capitalizes the apothegmatic big words:

We've all heard the saying A Picture Is Worth a Thousand Words.

Chicago's model example is:
The flag bore the motto Don't Tread on Me.
I'm about to add a sentence from a client onto ... heard of the phrase, a picture paints a thousand words.'

The second is definitely more idiomatic. "of" is odd here: one would more likely hear a phrase than hear *of* ... punctuation, too, and write the sentence as follows: We have all heard the phrase "a picture paints a thousand words".

To my ear, "We all have heard..." is an emphatic variant, such as might be used in a contradiction, and it would cause me to stress 'have' in speech. But I doubt if I'd use it. It's the kind of thing you might find in American computer manuals, like placing the adverb between the pronoun and the verb.
Mike.
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I'm about to add a sentence from a client onto a web page. I'm unsure which of these is correct. ... phrase, a picture paints a thousand words.' 'We have all heard of the phrase, a picture paints a thousand words.'

They are both grammatically correct, although I would, like you, tend to have used the second form. However, the "of" needs to go we haven't heard "of" the phrase, we've heard the phrase. Also, in my experience, the common expression has "is worth" in place of "paints."
Truly Donovan
Lexy Connor mysteries: Chandler's Daughter, Winslow's Wife http://www.trulydonovan.com
So Barnard may have helped popularize the expression but it doesn't appear that he coined either the "thousand" or "ten thousand" version.

Are we certain he wasn't the copywriter for the earliest cited ads?

The earliest citation I found ("'A look is worth a thousand words,'" say the Japanese") is from a 1914 New York Times ad for Shore Acres, a Long Island development of the real estate company Clifford B. Harmon & Co. It seems unlikely that Barnard, who managed a business that put ads on the sides of streetcars (Street Railways Advertising Co.) would have been involved in Long Island real estate advertising, but I suppose it's possible though I can't find anything on Barnard's career beyond Street Railways Advertising.
In any case, the story that is told on Daryl Hepting's website (also found in The Macmillan Book of Proverbs, Maxims and Famous Phrases , as well as a 1996 William Safire column) is that Barnard alone was responsible for coining the proverb for the 1921 and 1927 ads in Printer's Ink. The citations that I gave clearly show that various versions of the saying were floating around in the 1910s-20s, and it's improbable that Barnard was responsible for all of them.
I'm about to add a sentence from a client onto ... heard of the phrase, a picture paints a thousand words.'

They are both grammatically correct, although I would, like you, tend to have used the second form. However, the "of" ... the phrase, we've heard the phrase. Also, in my experience, the common expression has "is worth" in place of "paints."

Mr Love's proposed solution, or a variation on it, was clearly the best: 'We have all heard the saying, a picture is worth a thousand words', or capitalize the words in the saying, leaving off the comma as the CMS did.

Charles Riggs
My email address is chriggs/at/eircom/dot/net
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I'd be more likely to say, "We've all heard the phrase ..." than either of the above.

I agree. "We've all heard the phrase..."

Except it is more than a phrase. Calling it a 'saying' works well, being more poetic than calling it a 'sentence'.

Charles Riggs
My email address is chriggs/at/eircom/dot/net
This page: http://commfaculty.fullerton.edu/lester/writings/1000 words.html says that the characters shown in the picture are literally: A Picture's Meaning Can Express Ten ... see some great significance to this, but personally it seems like a normal variation on the usual saying, to me.

Wouldn't it be more correct to say a picture is worth 50 thousand words? Comparing the files sizes of a picture of decent quality with an ASCII file containing 50,000 words would be a closer fit than what tradition gives us.

Charles Riggs
My email address is chriggs/at/eircom/dot/net