[Mesorah] Hypercorrections or adaptation?

[Richard]

Baer P. 59 D"H HODU v'Chu'

V'taam ameeras p'sukkim halalu l'zeicher korban Tamid, kee v'somid shel shachar hayu om'rim hodu ad "uvinvee'ai al tarei'u..." 

Citing Seder Olam Rabbah 14.

Further 
The Ikkar would be to say it "meeyad" after "parshas hattamid... And so is minhag has'phoradim, but the Ashk'nazim preceeded it with Baruch She'amar"

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אמר ריש לקיש קשוט עצמך ואחר כך קשוט אחרים
בבא מציעא דף קז,ב
בבא בתרא דף ס,ב
Shalom, RRW