For a non-profit, what policy do you think is fair and sensible
regarding when to reimburse employees and volunteers for business
class travel (overseas, over X hours, never)? Thanks in advance.

Just a personal opinion from someone who has had many 9 and 10 hour
flights in tourist class:  it is entirely adequate.
Sure, business class is more comfortable and may be justified for
business travelers who are going straight to a meeting, but that is
the for-profit employer's decision.  The non-profit organization
cannot justify that, IMHO.
If the person would be going straight to a meeting, it would be much
cheaper to send him/her a day earlier and pay for an extra hotel night
 - and s/he would be in better shape for the meeting.

First and Business Class travel is very pleasant
- and a total waste of money

Give them a few Temazepan pills (short half life Valium) and use the
non-profit's funds sensibly.