What is the origin of the expression hashing out plans? I can't find a definition when googling for:
definition "to hash out plans" definition "hash out plans" definition "hashing out plans"
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The original meaning of the word hash was "to hack, chop into small pieces" from the French hacher, from Old French hache meaning axe. It often had culinary use, a hash being a chopped up mixture of things, most notably the dish hash browns, made of shredded potatoes. The expression to make hash out of sth/sbd, means to ruin sth/sbd and this follows logically from chop into small pieces
There is a derivation rehash, that dates from 1822, meaning talk over, discuss again or present in another form.
Later, hash over appears and although I cannot find a precise date, it seems to appear before hash out. The meaning is somewhat similar to rehash. A similar expression thrash out, had already been used for some time to mean working through the details of something and derived from the threshing of cereal crops to separate out the grain.
From around the 1940s I found some uses in google books of the form to hash out problems/differences, meaning to settle an argument through extensive debate. It seems a natural progression given the other expressions presented here. In modern usage hashing out plans/ideas still implies vigorous discussion but isn't necessarily an argument.
I offer a complementary view on the evolution of the phrase: rehash → hash over → hash out. Although the similar "thrash it out" may have influenced the phrase, it seems possible that the two phrases developed mostly independently, in parallel.
I couldn't place the origin of "thrash it out" as an idiom, but it may be as old as the metaphorical sense of separating wheat from chaff. The literal difference between thrash and hash is clear, though. So, how (or when) did the meanings dovetail?
The Monthly Review, a 1789 literary journal published in London, offers this example:
[H]e preserved too much professional dignity to exhaust himself through the press; he did not hash out and dress up the same things in different modes and forms [. . .].
Admittedly, this is a single data point—it may not constitute idiomatic precedent—but here we see the description of a rehash (which "he" refrained from).
In 1840, Harriet Beecher Stowe's essay "Love Against Law" (or "Deacon Enos") was published:
[T]wo days after the funeral, (for I didn't like to go any sooner,) I stepped up to hash over the matter [of a land dispute] with old Silence [. . .] and so I thought I'd speak to old Silence, and see if she meant to do anything about it, thought I knew pretty well she wouldn't; and I tell you, if she did'nt put it on me! we had a regular pitched battle [. . .].
This instance carries essentially the same meaning as "hash out" does today.
I don't think the transition to out is necessarily due to "thrash it out" (implying Americans simply dropped the t and r?). We have similar constructions like "walk it off", "talk it over", "work it out" and so on. Rather than a deviation, it may be that "hash out" was one idiom that developed in its own right and became popular whereas "thrash it out" never caught on—or at least died out after it did (vice-versa in British English).