I think that's part of the problem.
The premise that I do support is increased adoption. You know, more convenient hours for working families, better advertising, better behaviour analysis and training. All those things that help get animals out the door, so they don't have to go out the back. Really, 'pro-adoption' cuts to the point much better. You don't get anywhere by saying you're against something and leaving the alternatives in the details. You make progress, and earn mindshare by supporting something.
Because, really, if all you cared about was 'no more killing cute fluffy animals' it'd be fine if you warehoused them, or turned away all but the best prospects, or did any number of illogical things. And by saying that 'no kill' is the foundation of your beliefs, you're leaving the uninformed public to figure out how to do that. And they'll probably think of the first things, and write you off as stupid, crazy, or both. And they might not be wrong.
But, 'pro long term adoption', well, there's your solution right there! That's what you're trying to achieve, that's how you're going to do it. That's a positive, meaningful, unambiguous title.
Imagine driving by a shelter that had a big sign: 'This is a no kill shelter!' you probably cringe, thinking 'oh yes, they do have to kill poor fluffy puppies in shelters sometimes. But I'd rather not think about those things ... maybe I'll go to a nice friendly pet shop or neighbor instead where they won't bring up unpleasant topics like that ... unless some no-kill wacko catches me on my way in'
On the other hand, drive by that same shelter, with the same policies, but the sign instead says 'this shelter supports long term adoption!' well, yes, that's what you want, you want a place that is going to help you have a happy long term relationship with your pet. Maybe it's worth a look, since they seem so supportive and all.
Any term can get damaged by association (see pro-life/pro-choice) but this isn't even a cover. This is the unspoken core. Why go with a gloomy, ambiguous term like 'no kill' when what you're really about is 'pro adoption'?