In Middle English, amyddes is a locative adverb with a genitive -s ending meaning ‘in the middle’:
277: Bachus..sat hire besyde And Ceres next..amyddes lay Cypride. — Chaucer, Parlament of Fowls, c. 1382.
While even in Chaucer the adverb had also taken on the function of a preposition, the word was occasionally augmented with of:
A.2009: Amyddes of the temple sat Meschaunce. — Chaucer, Knight’s Tale, c. 1385.
4.2871: Evere amiddes of mi tale I thenke upon the nyhtingale. — Gower, Confessio Amantis, 1395.
1.2230: Amyddes of þis ilke tweyne..Stood Medea.
1.4217: Amyddes of þe feld. — Lydgate’s Troy Book, c. 1425.
This usage is also echoed in Early Modern English:
Vnto the woods runs loue, as well as rides to the pallace, neither he beares reuerence to a prince, nor pitie to beggere but (like a point amidst of a circle) still of an euennesse, all to a lesson he drawes, neither hills nor caues can auoyd him. — Robert Albott, England’s Parnassus, 1600. EEBO
Amidst of this horrid and affrighting confusion, merchants and well-meaning citizens remained in the most astonishing apprehensions imaginable … — Paul Rycaut, The History of the Turkish Empire, 1680. EEBO
I found by her words I her heart could command, so quickly we setled the matter in hand: we rambled about, till we came to a gate, where abundance of rabble peep’d in at a grate, to gaze at the ladies amidst of their revels, as fine all as angels, but wicked as devils. — Edward Ward, A Walk to Islington, 1699.EEBO
And, yes, the revelling ladies are engaged in, as one might suspect, the oldest profession.
Attestations in the early 19th c. are rather sparse, but one source criticizes the usage:
Amidst the crowd, not amidst of the crowd; because derived from the superlative adjective middest. — The Monthly Magazine, 11 (1801), 291.
The etymological explanation is inaccurate, but enough people must have been using amidst of to warrant a prescriptivist admonition.
Later in the century, however, William Morris becomes especially fond of the construction, although, as you noted, he also employs amidst without the supplemental preposition:
Thou hast seen my sword glimmer amidst of the moonlight,
As we rode with hoofs muffled through waylaying murder. — William Morris, Love is Enough, Or, The Freeing of Pharamond: A Morality, 1873, 55.
Now the men of God-home marvelled, and gazed through the golden glow,
And a man like a covetous king amidst of the hall they saw; — William Morris, The Story of Sigurd the Volsung and the Fall of the Niblungs, 1877, 100.
Within under the Hall-Sun, amidst the woven stories of time past, sat the elders and chief warriors on the dais, and amidst of all a big strong man of forty winters, his dark beard a little grizzled, his eyes big and grey. — William Morris, A Tale of the House of the Wolfings, 1890.
Morris uses the construction no less than ten times in his 1876 translation of the Æneid, one imagines, as an archaism. In fact, Morris’ preference for amidst of so warps a Google Book search that it renders the graph pointless for determining frequency.
While the construction does offer the advantage of an extra syllable while composing verse, one suspects that his choice of amidst of is to evoke an air of great antiquity, even if some of his translations are of works that predate anything one could call English.