In an exercise where the Solfege syllables are arranged low-to-high, should I transcribe the parallel low-to-high as well, i.e., Tenor-Alto-Soprano as below, or should I rearrange the presentation of notation to match the expected SATB arrangement?
It's quite unorthodox to mix the choral format with the piano format - I wouldn't attempt that, actually. I would treat the upper line labeled voice as a single part with the "tenor," "do," "alto," "mi" etc. as word sign expressions before the notes to which they apply.
Unless this is specifically meant to be sung by a choir with each person taking a separate note, I wouldn't try to turn it into a choir piece. It's more comprehensible to describe in a short TN before the example that the part labeled voice is transcribed as the right hand and then explain what you're doing with the text/labels.
If you feel you must transcribe it as individual voices with added rests, you'll need to treat the whole thing as ensemble format, not a blend of piano and choir. You can find the format description in MBC2015 Section 33. If this is the way you're going to go, also refer to section 38 and use the solfège syllables as text rather than placing them underneath the parallel.
I think just doing it as piano format is cleaner, but it's hard to judge without knowing the context of this particular example.