The question is expressed in terms of orthography: how was the possessive written? But I think that a related question is also worth investigating: how was the possessive pronounced in the poetry from Chaucer to the Elizabethans?
Poetry often preserves old forms of pronunciation, so that a feature may linger on in verse when it has already disappeared from common speech. You may be familiar with the case in French, where the “mute e” is no longer pronounced in everyday language, but continues to be pronounced in verse and songs, so that “flamme” is pronounced [flam] but may become [flamə] in song. Something similar was going on with Chaucer and his contemporaries like Gower:
it is worth emphasizing here that in the colloquial language of the period, final unstressed e [ə] was dying fast; some speakers probably used it only in set expressions like atte laste, to bedde, in towne, etc. Chaucer, however, continued to use the obsolescent pronunciation of final [ə] as an important metrical device.
Helge Kökeritz (1978). A Guide to Chaucer's Pronunciation, pp. 10–11. University of Toronto Press.
This applies to the possessive too, so that although the older form [əz] was already on its way out when he was writing, Chaucer consistently uses it in his poetry. I’ll give six examples from the General Prologue to the Canterbury Tales:
And specially from every shires ende
Ful worthy was he in his lordes werre,
That Cristes gospel trewely wolde preche;
That swich a lewed mannes wit shal pace
That hadde a fyr-reed cherubynnes face,
And in a glas he hadde pigges bones.
Geoffrey Chaucer (c. 1400). The Canterbury Tales, General Prologue. Wikisource.
Scan these lines and you’ll see that each requires the possessive ending on the word I’ve marked in bold to be pronounced [əz], as indicated by the spelling “-es”.
Unfortunately scansion ceases to be such a useful tool when when we come to the generation or two of poets following Chaucer and Gower, because iambic verse fell out of fashion, and poets such as Henry Lovelich (fl. 1450) and John Skelton (c. 1463–1529) used accentual verse instead, with a variable number of syllables per line, making it hard to deduce the pronunciation from the scansion. The evidence from Lovelich, writing in the mid-15th century, suggests that poets of this period could choose whether to pronounce the possessive ending as [əz] or [z]/[s] according to the needs of the line. I’ll give three examples from Lovelich’s Merlin:
that non Man scholde be born of wommans body,
and ʒe ben ordeygned for Mannes kende,
thanne sette he this Maydenis herte on fyre
Henry Lovelich (c. 1450). Merlin. In Ernst A. Kock, ed. (1904). Merlin, a Middle-English Metrical Version of a French Romance. Early English Text Society.
In the case of “wommans”, the rhythm and spelling go together to indicate that the pronunciation is [z]; in “Mannes” the rhythm and spelling go together to indicate [əz]; and in “Maydenis” the spelling suggests [əz] but the rhythm suggests [z] so the case is uncertain.
It’s not until Henry Howard, Earl of Surrey, writing in the mid-16th century, that we find verse that scans regularly again, and Surrey nearly always requires [z]/[s] for possessives:
Of our mishaps, and Troyès last decay
Rich, and of fame, while Priams kingdom stood
Hidden behinde her targettes bosse they crept.
They sayd Lacons desertes had derely bought
Her prophetes lippes yet neuer of us leeued
When the kinges ship put fourth his mark of fire,
The right, and faith, my Hectors bloodless corps
Henry Howard, Earl of Surrey (c. 1540). The Second Boke of Virgiles Aenæis. In Samuel Johnson, ed. The Works of the English Poets from Chaucer to Cowper, volume II, pp. 338–345. London: J. Johnson etc.
In this work, the only word that needs the old pronunciation is “Troyès”, which the editor has marked with an accent.
Putting this together, between 1400 and 1540 the pronunciation of the possessive as [əz] gradually became too archaic for use by poets, but the paucity of regular verse in this period makes it hard to trace this process. Spelling took even longer to catch up: you can see that Surrey wrote “targettes”, “prophetes” and “kinges” even though he no longer pronounced the e.