The Times (of London) only has one reference to shouting from the rooftops, from the 1950s, but it has several, all early 20th century, to “from the housetops”, or house tops, or housetop, and so on, although what people should do, or not do, ranged from preaching through trumpeting to proclaiming:
Wednesday, May 03, 1905; pg. 7 “The duty of cleanliness should be preached from the housetops”
Saturday, May 11, 1912; pg. 10 (in an advertisement) “There is no need to proclaim from the house tops the merits of a good article.”
Thursday, Sep 30, 1920; pg. 5; “… their good work in the district is generally known to people who do not care to declare it from the housetops.”
Tuesday, Feb 12, 1924; pg. 14 in an advertisement, quoting the Daily Graphic: “The beauty of the book ought to be trumpeted from the housetops.”
and once in the singular: Friday, Mar 23, 1917; pg. 9, in another book ad: “Occasionally, very, very occasionally it happens that a book appears whose merits one would like to shout from the housetop ...”
It looks, therefore, as if the original idiom did indeed echo the Bible and used “housetops”, not “rooftops”, but I’m surprised at the lack of 19th century examples, and the absence of anything after 1924.