What is the origin and meaning of "Save some for Jehoshaphat"?

The most familiar context in which Jehoshaphat (or Jehosaphat or Jehosophat or Jehoshophat) appears in early twentieth-century U.S. English speech is in mildly euphemistic exclamations such as "Great Jehoshaphat!" and "Jumping Jehoshaphat!" and "Great jumping Jehoshaphat!" and "Holy Jehoshaphat!" and (in at least one instance) "So help me Jehoshaphat!" In each case, Jehoshaphat stands in for God or Jehova or Jesus, presumably because taking the name of an ancient king of Judah in vain was considered relatively unobjectionable.

But that usage, though it certainly familiarized people in the United States with the word Jehoshaphat, does nothing to explain why someone would say "Save some for Jehoshaphat" at Sunday dinner. In searching Google Books for a cultural reference that might have led to that phrase, I found only one remotely plausible candidate.

In 1921, a poem featuring a farm horse called Jehosophat (or Jehoshaphat) became very popular throughout the rural United Sates (and parts of Canada) as an expression of tenacity, determination, and an indomitable spirit. Among the many periodicals that reprinted it was Hettinger's Dental News (May 1921), which ran it under the title "Jog On Jehosophat," and attributed it to "Griff Crawford, in "The Gloom Chaser.'" In the poem the speaker clucks to his horse and urges it forward despite a litany of troubles that leads him to say, at the end of the first verse:

Looks some gloomy, I'll admit—

(Cluck!) Jog on Jehosophat, we ain't down yit.

At the end of the second verse, the speaker again refuses to be down-hearted:

No use stoppin' to de-bate—

Jog on Jehosophat, it's gettin' late.

Then about midway through the third verse, the speaker begins to believe that things may work out after all. Here's the entire third verse:

Wheels all wobble; axle's bent;

Dashboard's broken; top all rent;

One shaft splintered; tother sags;

Seat's all busted; end-gate drags;

May hang t'gether—b'lieve it will;

Careful drivin' 'ill make it still;

Road's some better, not so rough—

TROT! Gosh ding ye! That's the stuff,

Old trap's movin,' right good speed—

(Cluck!) Jog on Jehosophat, you're some old steed.

Road's smoothed out 'till it don't seem true—

(Cluck!) Jog on Jehosophat, you pulled us through!

In Google Books search results, this piece shows up (with different titles, attributed authors, and spellings of Jehosophat/Jehoshaphat) in such periodicals as Manufacturers Record (March 17, 1921), The Peanut Promoter (April 1921), The Natural Gas Industry (June 1921), The Associated Grower (August 1921), The Oil Mill Gazeteer (October 1921), The Kiwanis Magazine (November 1921), Implement & Tractor Trade Journal (December 17, 1921), The [Hudson's Bay Company] Beaver (1921), The Swine World (January 5, 1922), Normal Instructor and Primary Plans (April 1922),Motorcycle & Bicycle Illustrated (April 22, 1922), [National Fertilizer Association] News Bulletin (June 1922), and Annual Report of the Indiana State Dairy Association (1923[?]).

It then had a resurgence of popularity in the early 1930s, appearing in The Dairyman's Monthly Review (1932[?]), Nulaid News (1932)[?]), and The Cow Bell (1933[?]), as well as in one or more anthologies of optimistic or inspirational verse.

In Nova Scotia Department of Agriculture and Marketing, Report (1933) [combined snippets], a reviewer cites a recitation of the poem as a highlight of an evening's entertainment:

The monologue entitled, "Jog on Jehosophat", was one of the most appropriate and humourous numbers on the program. Jehosophat (a horse), harness, wagon and entire make-up represented a model of "Depression", still Jehosophat and his good owner D. R. rode along ambitious of attaining success, even if hard times prevailed.

A favorite poem of a person's childhood might have yielded a related saying in that person's household even decades later. In this case, "Save some for Jehoshaphat" might be understood as meaning "Save some for when Jehoshaphat finally arrives"—not so that the horse could eat the food, but so that the person driving the decrepit cart could.

It's somewhat far-fetched, but at least this explanation connects the name Jehoshaphat to something other than a long-dead king (whose eating habits are not recorded) or a biblical valley. However, I couldn't find any evidence that the expression "Save some for Jehoshaphat" was ever in widespead use. The entry for Jehosaphat in J.E. Lighter, The Random House Historical Dictionary of American Slang (1997) cites the term only as a euphemism for Jesus or Jehova.