"Imaginatively" as a synonym for "in imagination"

I'm not sure why John Dewey says "in imagination" rather than "in the imagination". It seems rather whimsical but not wrong.

But "imaginatively" doesn't ever mean "in the imagination": it only means "in a way that is new, original, and clever" (Cambridge). The word needed is imaginarily.

If artists say "the beholder can rearrange the objects imaginatively" they are inviting us to take hold of the objects and redistribute them in a way that shows creativity or inventiveness! The quote about Glasgow is equally misleading.

The OED defines imaginary as "existing only in the imagination" and "imaginarily [adverb]" as a derivation.

I've resolved this by looking at a 1971 Compact OED. it includes the entry "Imaginatively adv. In an imaginative fashion; in imagination"

The example given is from William Petty (1662):

"A man is actually and truly rich according to what he eateth, drinketh, weareth, or any other way really and actually enjoyeth; others are but potentially or imaginatively rich, who though they have power overmuch, make little use of it; these being rather Stewards and Exchangers for the other sort, then owners for themselves."

(This text is to be found here: https://en.m.wikisource.org/wiki/Page:William_Petty_-_Economic_Writings_(1899)_vol_1.djvu/191)

It's just an old archaic sense of the word. So no surprise to come across it in scholarly/artsy writing.