What does spite mean in "spite of despondence" in the poem Endymion by John Keats?

The strongest argument for reading "Spite of despondence" as "In spite of despondence" is, as the poster points out, the follow-up usage of "in spite of" within the same sentence three lines later. Here again is the whole sentence:

Therefore, on every morrow, are we wreathing

A flowery band to bind us to the earth,

Spite of despondence, of the inhuman dearth

Of noble natures, of the gloomy days,

Of all the unhealthy and o'er-darkened ways

Made for our searching: yes, in spite of all,

Some shape of beauty moves away the pall

From our dark spirits.

Keats lists four things that might discourage a person from feeling bound to the earth through a love a beauty: (1) despondence; (2) a dearth of noble natures; (3) gloomy days; (4) unhealthy and darkened obstructions. But at both ends of this list he identifies things in opposition to those discouragements—first, the act of creating beauty ("wreathing a flowery band"), and second, the experience of feeling the force of beauty sweep away the cloud of gloom. Both positive things act contrarily and counter to the negative forces—which is to say, both act in spite of them.

I checked a number of books that quote this passage of Endymion, and most of them don't provide any commentary on the line in question. This, I think, is because most of them have no question that "Spite of despondence" means "In spite of despondence." I did find three texts, however, that venture a restatement or gloss on the original wording. From Milton Goldberg, The Poetics of Romanticism: Toward a Reading of John Keats (1969) [combined snippets]:

Mind and heart must interact to sprout a soul. Emulating the sweet sonnet, fettered in spite of loveliness, we must wreathe a flowery band to bind us to the earth—in spite of despondence or the dearth of noble natures:

If by dull rhymes our English must be chain'd,

And, like Andromeda, the Sonnet sweet

Fetter'd, in spite of pained loveliness;

Let us find out, if we must be constrain'd,

From Origins, volume 24 (1995) [combined snippets]:

He goes on to ask, in his classic poem, Are we creating some beauty each day ... in spite of despondence or the dearth of noble natures?

And from Keki Daruwalla, Poetry Magic 7 (2005), a collection of poetry designed for "the young":

Spite of despondence, of the inhuman dearth

[Explanatory note:] SPITE OF DESPONDENCE: in spite of being gloomy

This is not to say that Keats only uses spite to mean "in spite of." Michael Becker, Robert Dilligan & Todd Bender, A Concordance to the Poems of John Keats (2016) notes two other occurrences of spite in Endymion—in Book 3, line 615:

"Young lover, I must weep—such hellish spite

With dry cheek who can tell?

and in book 3, line 650:

I saw grow up from the horizon's brink

A gallant vessel: soon she seem'd to sink

Away from me again, as though her course

Had resum'd in spite of hindering force—

The "hellish spite" is unmistakably maliciousness, and the later "in spite of" clearly functions in the sense of "notwithstanding."

In books about Endymion, the "Spite of despondence" line seems uncontroversial. The few texts that address it at all interpret it as meaning "In spite of despondence," but most don't comment on it at all. The first law of poetry is that nothing is certain, so people who interpret the line differently are exercising their muse-given right to do so. But I think that the poster's reading of the line is the most straightforward and coherent of the various readings that are possible.