Some of the most beautiful and challenging religious literature in history comes from medieval Europe, and 13th-century quasi-nun Mechthild of Magdeburg's Ein Vliessende Lieht der Gotheit (Flowing Light of the Godhead) is among the best. (I'm not at all biased here.) Her book of mystical poetry, luscious divine visions, and apocalyptic prophecy is also a benchmark in the history of women's writing, later medieval theology, lay people seizing control of religion for themselves, and the serious use of the vernacular (non-Latin) for religious writing aimed at a wider audience. 19C-early 20C German scholars even hailed it as a major development in the history of the German language.

Unfortunately, OP is correct: even though three different versions of the FLG survive--two in Middle High German, one in Latin--none of these is the original. Mechthild wrote in the language of later medieval northern Germany, Medieval Low German.

To offer some background: there isn't a clear linguistic distinction between MHG and MLG; it's more like a gradient from medieval High German to Low German to Dutch, with all sorts of dialects and entirely unstandardized spelling. Still, a gradient implies distance--the language spoken/written in Magdeburg was not identical to what people were using in Nuremberg or Deventer.

Additionally, scholars have noted fairly distinct literary cultures in terms of a lot of the texts that circulate, particularly religious texts. The theological style of Mechthild's mysticism is definitely more related to the northern/Dutch tradition.

So anyway! the reason we know none of the three surviving version of the FLG is the original is either really cool or really boring: the translators flat-out tell us.

First, the preface to the late-1200s Latin version reports that the book was "written in a primitive tongue." That doesn't clear up the Low German versus High German (southern/central) division, but it does mark the book as a (claimed) translation from the vernacular.

Second, one of the MHG versions is clearly a translation back into German from that Latin version, so it's not a candidate to be the original.

Now, the MHG version that scholars study as essentially Mechthild's was given to the 14th century nuns of a Swabian convent called Maria Medingen by an external priest named Heinrich von Nördlingen. He was a frequent letter correspondent and spiritual advisor to some of the sisters at Maria Medigen and the convent of Engelthal near Nuremberg. In his letter that apparently accompanied the delivery of the FLG, he praises the book lavishly, but adds:

Whichever words you do not understand, indicate them and write to me. Then I will translate them [into German] for you, because it was lent to us in such a strange German ("tützsch") that we spent two years of hard effort and work before we brought it a little into our German.

Setting aside that MHG and MLG are not that different from each other (although Mechthild's use of language can be challenging and increases the difficulty of proper translation; her modern translator Frank Tobin has discussed this), Heinrich's statement places the manuscript that he and his circle used as MLG.

But this is where things get interesting.

The Maria Medingen MS, and hence the translation, is from the mid-ish 14th century, long after Mechthild's death. The Latin translation dates to the late-ish 1200s, and claims to have come originally from Mechthild and her confessor (priest-advisor). Since it is missing the seventh "book" that Heinrich's MS has, it seems reasonable that the Halle brothers obtained their copy while she was still writing it.

So how do we know Heinrich's source MLG manuscript was actually Mechthild's original?

The major MHG version of the FLG and the Latin version are significantly different beyond just the MHG's inclusion of a seventh book. In fact, it's to the point that scholars typically refer to the Latin by its own title, Lux divinitatis.

The first clue that places Heinrich's MS source as the/very close to the original is the structure of the text. The FLG as a whole is made up of short poems, descriptions, visions, and theological investigations put together as an anthology, divided into those 6/7 books. In the MHG version, there's an identifiable progression of mystical theology over the course of the book as a whole, but otherwise it's sort of a topical mishmash--a logical result of a book composed over decades, and probably with some of the material shuffled around at various points. The Lux divinitatis, on the other hand, has a more surface-level coherent organization.

The difference suggests that the MHG text (translated from MLG) is closer to the original than the LD. More generically, it shows us one of the types of changes that people willing to alter the text would be interested in making: making the thing make more sense when read through. So it makes sense in general that the MHG MS reflects the original text in this regard.

Second, the MHG version and Latin LD have some different contents, too. As a major player in the history of not just mysticism but bridal mysticism, Mechthild's employment of the Bride of Christ allegory to frame the relationship of the soul with Christ sometimes ranges into the quasi-sexual:

In this utter blindness she sees mostly clearly

in this pure clarity she is both dead and living.

The longer she is dead, the more blissfully she lives.

The more blissfully she lives, the more she experiences.

[...] The deeper she dwells, the more she expands

The deeper her wounds become, the more violently she struggles

The more loving God is to her, the higher she soars

The more his desire grows, the more extravagant their wedding celebration becomes

The narrower the bed of love becomes, the mre intense are the embraces

The sweeter the kisses on the mouth become, the more lovingly they gaze at each other

The greater the distress in which they part, the more he bestows upon her

The more she consumes, the more she has

or

[The Soul speaks]

"I cannot dance, Lord, unless you lead me

[...] Then I shall leap into love

From love into knowledge, from knowledge into enjoyment

And from enjoyment beyond all human sensations

There I want to remain, yet want also to circle high still"

And the young man has to sing thus: "Through me into you, and through you from me."

[...] The young man speaks: "Young lady, you have done very well in this dance of praise. You shall have your way with the Son of [Mary], for you are delightfully weary. Come at noontime to the shade of the spring, into the bed of love. There in the coolness you shall refresh yourself with him.

There I'm borrowing Tobin's translation of the MHG Maria Medingen MS. I don't have the original LD in front of me (and I don't think there's a published translation). But suffice to say: some of Mechthild's more searing bridal language is neutered.

This difference is extremely telling that Heinrich's source MS was very close to the original, especially compared to the LD. It's not a question of the impossibility or unwillingness of medieval translators/copyists to add or alter erotic/quasi-sexual language of the original. A few decades before Mechthild, Beatrijs of Nazareth's hagiographer (spiritual biographer) did something along those lines with her Dutch treatise On the Seven Manners of Loving.

Instead, we look to one of the major differences between the use of the vernacular versus Latin in later medieval religious culture. Namely, Latin was the language of official recognition. If Mechthild's supporters (who translated the text) wished to preserve her legacy, not just translating it into Latin but shaping it into less challenging (theology-wise) Latin was a good move. (This might also be a factor in the LD's lack of a seventh book, which scholars generally consider the most theologically daring.)

So once again, we're left with the point that Heinrich's text does include the more baldly quasi-sexual language that was potentially problematic, and that some people who got their hands on the original FLG would wish to change.

So in the end: the ability of internal and external clues to place Mechthild near the MLG-speaking Magdeburg, the declaration of all surviving editions to be a translation, the closer proximity of the Maria Medingen MS to the original, and Heinrich's label of "strange German" suggest that Mechthild wrote in Middle Low German, and that we can take the nuns' text as more or less her writing and meaning in translation.