Leaving aside the terminological difficulties inherent to the name "Vulgar Latin" (of which I am sure you are aware already), I would suggest that the begining of the sixth century is perhaps too late a target date for an "undifferentiated" Vulgar Latin: epigraphic evidence suggests that by this point some of the main isoglosses separating the various Romance varieties were already solidly in place. On the other hand, if you go back to (say) the end of the first century, while you have a largely "undifferentiated" VL, you also have something which is simply a slightly more analytical version of Classical Latin, complete with case inflection, vocalic quantity and all.
Were I to attempt a translation such as this, I'd probably prefer to pick a target place, as well as time. Perhaps
Desiderata as translated by someone living somewhere in Provincia Narbonensis. This variety could be considered ancestral to the Gallo-Romance group, comprising the Oïl and Oc dialects of France, Rhaeto-Romance, Catalan and the "Gallo-Italian" languages. Therefore we'd be looking at a variety which has the collapse of the CL vowel system, intervocalic lenition and merger of "palatals" derived from CL /tj/ and /kj/, but before such differentiating changes like tonic diphthongisation of mid vowels.
As an example of what we're discussing, let us take the first sentence of the poem. For the variety described above, I would suggest something like the following translation:
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u̯áða kon kálma tọon kamíno ẹ́ntre el rumọ́re e la frẹ́χta,
e sou̯ę́n′is-te de la pádze kẹ́ pǫ́des enkontrár en silẹ́ntso.
The orthography used is not exceptional in Romance studies: the underdots indicating mid-close vowels, while the caudae indicate mid-open vowels. The prime symbol ′ marks palatalisation. I've tried to stick to those words attested in all of the daughter languages, although I am somewhat dubious about
frẹ́χta for "haste", as it only appears to be attested in this sense in Italian
fretta.