There's another way to look at "acceptance" and that is, not as resignation, but simply as a necessary stepping stone for dealing with reality. If the reality is that a person is depressed, how can they work to change a reality that they don't even accept is real?

Telling oneself that it's not so (the opposite of acceptance) may work for some, may work for a while, but it also may just be a band-aid. I've actually done it with success.. fake it til ya make it! However for me it's a method that works a helluva lot better when I'm just "feeling a little down", than when I'm actually clinically depressed.

In order for the methods of a person such as the guy you referenced earlier, to qualify them as having "better" compassion, it would be necessary for those methods to work universally, and I think it's a mistake to suggest that there is any single solution that will work for everybody. We are each the result of so many factors: our genetics, our environment, our history.. I think if something works better for you and others personally (and as I've never seen you present these ideas in any way but the abstract, so I'm not even sure you're saying that), then that simply makes it better for those people it works for. More power to you if that's the case.

What I do think speaks to the quality of a person's compassion is that they do share what works for them, so that others who might be helped by that information have that chance. Still doesn't make their compassion "better" though.. and I confess I don't quite understand what compels you to make those distinctions.

I doubt very highly that anhedonia ever exists in a vacuum; it's a characteristic of many disorders, and those disorders become trickiest for us when comorbid with other conditions. I don't personally know anybody with the luxury of just one. As such, I think there's very little likelihood that there is some perfect methodology that will work universally for everyone affected; if there was, it would probably not exist as a public health problem at all.