My ds (5) also has it, and has gotten hysterical when I tried to give him the drops. He's also sick with a double ear infection and a very bad cough, and he's getting amoxicillin because this has become protracted and nothing else is helping. So I decided not to push the drops and see what happened. It is now clearing up on its own. Today I didn't see any evidence of it in his eyes. How bad is your son's pink eye? My ds' was fairly mild, so I wasn't overly worried about delaying the drops and seeing what happened. Now I don't know if the amoxicillin is treating it anyway (he'll take that without a problem).
Could you call your ped and explain the problem, and find out if you are doing anything harmful by not giving the drops? If it just takes longer to clear up and wouldn't cause lasting damage, I'd let it go. I know from reading your posts that you are an incredibly respectful mama, and that you would be honoring his distress rather than "giving in." If, however, this could affect his eyesight in the long run I'm afraid there is no choice but to make him take the drops (easier said than done!) I suspect, however, that it's more of an annoyance illness than anything else.
Hope you can resolve this for your little guy's sake, not to mention yours!