I think we're going in circles here. I'm agreeing with almost everything you're saying; I think we're just using different terms for the same thing and the same term for different things.

Trying to make my point as simple and brief as possible: if I see someone hurting, I get a small twinge of sympathetic pain. That pain sparks the conscious response, "What needs to be done in order to help this person?", and I start to think about how the problem arose, how to fix it, etc. If I see someone who was in pain and now has been helped by me, I feel a small spike in sympathetic joy.

I have no particular problems with this particular mental algorithm. But, the group of Buddhists I was talking to said that this algorithm was bad, and that I should get rid of it. My understanding from what you've said, and what other people have told me, is that this not the position of most Buddhists. Since that qualm about Buddhist meditation practices has now been satisfied, I'm looking forward to reading the rest of the posts in this sequence.