Maybe a solution to your banning problem could be to create a federated "FeelBetter" group of people who would be willing to automatically grant a few of their tweets. So you build an app that posts a FeelBetter message as one of the member of the group, in rotation. Kind of Seti@Home but for twitter tweets. The tweet would relate to the whole group something like: "@Recipient hug from me and the @FeelBetterBot community"
I'd be more concerned that you get hacked like buffer did a few days ago and you start sending bad tweets as the members :) but besides that I'd be willing to "donate" a few of my tweets to this do-good project
I think the automatic bot style is the way to go. The importance is not the "really thought out message" that someone can send, while rather the low latency, the immediacy of the reply to those that need it. So timing is more important. At least this is what I felt from the positive comments you showed off in your blog post. :)