In reply to:

It is often possible to reconstruct a sentence to use general plurals or avoid pronouns, but I am interested in the board's opinion for the occasions when gender neutral pronouns are necessary. Do you prefer "he or she" "he/she" "his/hers" or do you (like me) [putting his cards on the table e] prefer using "their" "they" as gender neutral singular pronouns?

I refuse to use the virgule version or to apply a plural pronoun to a singular noun. I tend to rewrite sentences to avoid those choices, and if presented with an unavoidable use of an indeterminate-sex-singular-pronoun I usually use simply, "he." Occasionally, when the subject of the writing pertains overwhelmingly to women, (such as when referring to rape victims or spousal abuse victims) I use "she."