Still no on all counts. I'm a CON and a "healer" at that (not that there's a clearly defined line for which casters are healers and which aren't) and I don't mind the cure/-ga hate at all.

The tank keeping hate also isn't solely his/her job. If a caster gets high hate because they had to cure more than anticipated to prevent a death, have someone in the green use accomplice on them to balance it out a bit so they can get back to healing. Yes, the ideal is just to stop healing for a bit but that's not possible 100% of the time without exception. In a team/party environment it is a team effort and spot assists where needed bridge the gap just fine.