What is the ruling on writing part of a verse or a word from it, for the purpose of solving a Tajwid assignment, or for correcting a recitation later?

There is no harm in limiting the examples for rules to one or two words, and this is what authors in Tajwid and Qira'at have consistently done. An example of this is what Al-Shatibi mentioned in "Hirz Al-Amani" when discussing the detached (munfasil) and connected (muttasil) madd, and the softening (tashil) of the second hamza when two hamzas occur in one or two words.