The reason this problem arises is that the consonant in the middle of usual - which phoneticians call the voiced palatoalveolar fricative, and which is written in the International Phonetic Alphabet (IPA) as [ʒ] - doesn't have a fixed representation in the English writing system. When it occurs in words borrowed from other languages, we usually keep the original spelling (luge, rouge, gendarme) and when it occurs in a native English word, we write it with an S (measure, usual, pleasure). In particular, it never occurs at the end of a native English word, only in loanwords like luge.
In any case, it's relatively rare in English (loanwords or no), so as English readers and writers we don't have much data from which to conclude what the "best" or "most common" way to write [ʒ] is.
Therefore, when truncations like as per usual -> as per yuʒ occur (a problem which, by the way, is not unique to "as per usual" - as this previous question reveals, the common slang phrase business caʒ for business casual has the same orthographic difficulty) the only unambiguous way to write it is to use that IPA character, ʒ.
Since, obviously, most people can't read IPA, the question boils down to "how do I write a sound that my language's writing system doesn't let me write?" You're stuck with a large variety of more or less confusing approximations:
- uzh / yuzh (my personal preference); zh is a logical way to write [ʒ] since it is the voiced counterpart of the English sh sound (in layman's terms, zh is to sh as z is to s).
- uge / youge / yuge, by analogy with rouge, luge, and (approximately) huge.
- and any of the other suggestions in the comments above
Ultimately, this question can't be answered without considering why and for whom you would write such a thing down, anyway. It's an almost exclusively spoken form. In those rare situations which would force you to write it - dialogue for a novel or screenplay, let's say - the most you could do is probably just choose one of the above options and hope your audience is familiar enough with the construction to figure it out.