www.alphadictionary.com

Came across ‘hope springs eternal’, and got to wondering if ‘eternal’ is ‘officially’ an adverb, as is ‘slow’.
Well, it is in the OED, but under ‘quasi-adv.’
Is this a generally accepted way of saying, ‘yeah, but in the way of poetic license’?

Okay, did some more research:

“In some unrevised OED entries, quasi- (meaning ‘having some but not all of the properties of’, ‘almost, virtually’) is used to modify grammatical terms. For example, a sense of a noun might be described as ‘quasi-adj.’, indicating that the noun is being used as if it were an adjective, or is very close to being an adjective. In revised entries, this term is not used: a word behaving as an adjective, for example, is treated as an adjective.”

Came across ‘hope springs eternal’, and got to wondering if ‘eternal’ is ‘officially’ an adverb, as is ‘slow’.
Well, it is in the OED, but under ‘quasi-adv.’

To me, it 'feels' more like an adjective. 'Eternal' is what hope is, rather than how it springs. Compare the following:

He died happy.
The river ran dry.
They are sitting pretty.

Point well-taken. I think I was attracted to the more poetic reading.

But now I think of it . . . if the hope is eternal, why and whence is it springing?

Something like an everlasting fountain, perhaps? The fountain is eternal; the water springs.

Excellent point, although I’m not conceding.
Incidentally, the only citation of the phrase in the OED is in
Pope’s 1733 An Essay on Man.

I'd go with a simple poetically licensed shortening of 'eternally'. "Hope springs forever" doesn't quite cut it, does it?

But is it possible to spring eternally? 'Eternally' implies an unchanging state (e.g. 'exist eternally'), whereas 'spring' implies a change of state (an upward motion).

It is the unchanging state of being in spring. Ever rising.

Meanwhile, deeper in the weeds . . .

or, ‘eternal’ might be read as ‘continually’, rather than ‘continuously’.