Brad Hart pointed to a very valuable source that irrefutably proves the journal a fraud. From that source, Frank E. Grizzard's assessment in an email he sent to Ed Brayton:
"The so-called prayer journal is not in GW's writing, although I'm not sure it's actually a forgery. The manuscript dealer (Burk I think) who first sold it when it came to light in the 19th century printed a facsimile edition in which he admits that the Smithsonian rejected it as a non-GW document, but it did have Washington family provenance, so he said. Thus it apparently was a descendant's. Johnson's version is taken from Burk. The prayers are based on the English prayer book."
-- Frank Grizzard (senior associate editor of the George Washington Papers collection at University of Virginia) [in an email he sent] to Ed Brayton (2004).