"Handsome is as handsome does," and the puzzling use of "as"

When I saw the film Forrest Gump, I first heard the expression “Stupid is as stupid does,” and inferred that (to Forrest, at least) it meant something like “Don’t judge me stupid because of my words, judge me only by my actions.” This sense was not totally clear, because he said this expression to people who had in fact judged him by his actions. And what’s more, the wording of the expression did not seem very suitable to that message. It seemed about equally amenable to "Each of us is as stupid as the things we do," which at least made some use of that word "as."

Anyhow, the other day I was watching the much earlier film The Candidate, and someone asked a woman whether she found Robert Redford handsome. She responded “Handsome is as handsome does.”
I’d never heard that before, and it was news to me that this is sort of a set phrase, with different adjectives swapped in.

But today I’ve been looking into the expression on the web. I’ve found a lot of people there trying to puzzle out this weird construction. But here’s where things stand with me.

As the ancient adage is, goodly is he that goodly dooth. – A. Munday
View of Sundry Examples in J. P. Collier John A Kent (1851) 78, c.
1580

He is handsome that handsome doth. – N. R. Proverbs 49, 1659

To be sure, I never thought as it was any harm to say a young man was
handsome; but to be sure I shall never think him so any more now; for
handsome is that handsome does. – Fielding, Tom Jones (Book IV,
Chapter XII), 1749

They are as heaven made them, handsome enough if they be good enough;
for handsome is that handsome does. Goldsmith, Vicar of Wakefield, 1766

Mr. Digweed has used us basely. Handsome is as handsome does; he is
therefore a very ill-looking man. – Jane Austen, Letter to Cassandra
(1813-01-24)

‘They are – at first sight at any rate,’ laughed Pippin with a sudden
relief after reading Gandalf’s letter. ‘But handsome is as handsome
does, as we say in the Shire; and I daresay we shall all look much the
same after lying in hedges and ditches.’ – The Lord of the Rings, Book
One, Chapter 10, Page 170 Handsome is as handsome does. – Spirit of
Times 297, 23 Aug 1845

‘Don’t you think her much better looking than Alda?’ ‘If handsome is
that handsome does.’ C. M. Yonge, Pillars of House II. xvii., 1873

‘But he’s such a handsome, chivalrous, man.’ Handsome is as handsome
does, thought York grimly. A. Williamson, Funeral March for Siegfried
xxiv. 1979

So it appears that from the very start there was some ambivalence about adjectives and adverbs. But everyone before Jane Austin had “that” rather than “as,” going a long way toward making this construction understandable.

He is handsome that does handsome things.

Handsome is [he] that handsome [things] does

Handsome is that handsome does.

But since Jane, it’s been dicey.

Do I have this basically right? Is there a good story here about why Jane switched to "as," and why the switch prospered? Did she understand the expression some other way, or was the “as” construction somehow appropriate on the one understanding? I feel like I’ve heard British people in literature do this, using “as” where we would expect “that,” but as a mark of vulgarity.