Object pronoun ordering in imperatives has been a longstanding issue and is a lot less fixed than textbook grammars describe.

The prescribed standard is similar to the one described in the question’s first link: V – le/la/les – me/te/lui/nous/vous/leur – en/y, with -me and -te shifting to forms similar to their stressed outcome (-moi, -toi) when they occur last.

This would output "prends-t’y", which is indeed prescriptively standard. But there’s several problems with that:

• There’s a lot of variation in usage even without involving y and en, some of it dialectal, and you’ll encounter forms like "donne-me-le", "donne-moi-le" or "donne-le-me", even in literature (exemples taken from Le Bon Usage: "Rends-nous-les" (Hugo), "montrez-moi-la" (Proust), Di(te)s-nous-le (Hériat, Monterlant), Tenez-vous-le pour dit (Nerval, Renard, Gide, Mauriac, Cocteau)).
• In the standard, several pronouns change forms depending on their neighbouring context: -me and -te alternate with -moi and -toi depending on whether they’re the last element in the clitic chain, -le has a stable vowel (/lœ/, /lø/, /lɛ/ depending on the dialectal variant), i.e. "donne-le aussi" is pronounced /dɔnlœosi/, not */dɔnlosi/, which is what you’d expect if it was an unstable /ə/, but before y and en, this vowel elides as if it was /ə/ (amène-l’y) and finally y and en are often preceded by /z/ through liaison, which has prompted the generalisation of this liaison consonant to contexts in which there shouldn’t be one (va là-bas -> vas-y, which should in all logic be spelled "va-z-y")
• The rule saying that te and me + y or en give m’en/t’en/t’y/m’y is a generalisation of a phenomenon that could in the classical period mostly be observed with en only and with a limited set of verbs, most famously s’en aller (i.e. va-t’en). This generalisation never took: people find forms like achète-m’en or amène-m’y awkward, if not fully ungrammatical.

To fix the second problem, speakers have generalised one form in all contexts: the alternation between me and moi is abandoned and moi used everywhere (see the "donne-moi-le mentioned above) except in some regions where me is used instead ("donne-le-me"); le never loses its vowel (donne-le-z-y); and the z-liaison forms of en and y are generalised to every context (donne-leur-en -> donne-leur-z-en).

This is going to be extremely frequent, of course, with the very awkward moi+y/en and toi+y/en combinations, where sequences like "donne-moi-z-en" are regularly used instead of the prescribed but abnormal sounding "donne-m’en".

For "s’y prendre", this means "prends-toi-z-y", which is how I’d probably spontaneously form it.

But those forms are subject to some normative pressure, so some speakers take advantage of the variability in enclitic pronoun ordering (problem 1 above) to shift -moi and -z-y: Prends-y-toi. This allows them to use the regularised forms /mwa/ and /zi/ in places where they’re prescriptively licit (after a verb where you’d expect the z-liaison for -z-y and in the final slot of the pronoun chain for -moi). And indeed, like in reverso link, you’ll sometimes encounter speakers confidently stating that such forms are prescriptively licit, which they are not.