A little realpolitik talk.
If we're too aggressive/successful with the minor species on the border zone, we might provoke the war with the Cardassians into turning hot before we area ready. And we are so not ready. We have been warned a lot about that in the intelligence briefings, that there may come a point where if we are trying to 'save' everyone from Cardassian domination we will be forced into war. I wouldn't want to fight a war until four years out at the absolute soonest, and ten years would be far preferable.
And I know I'm going to get some pushback on this, but Cardassian domination probably isn't the worst thing in the universe. We're not dooming these species to being eaten by the Biophage or absorbed by the Borg. In all likelihood, they won't be occupied like Bajor was... that seems to have been something of an exception. It's more that they will secondary client state dominated by a strong neighbor, only able to take the mining/colony assets they are allowed to and making sure their foreign policy toes the Cardassian line. It's not hell.
So while we're not going to actively "give" groups to the Cardassians, maybe it wouldn't be the worst idea to make a list that we won't try so hard on with diplomatic pushes. Groups that the Cardassians can try with, feel like they're having a success, and not feel so pressured. That, more than anything else, would be a reason not to push the absolute hardest we can with all of the non-affiliate border states.
A lot of these minor powers have not-insignificant military assets of their own. If we get enough of them, the Cardassians would be extremely foolish to go to war. That said, we might not be able to get enough of them before the cardies panic and attack, so making a list of priorities would be a good idea.
Blue are people we can't give up, white are ones we can consider giving up, yellow are ones we shouldn't even bother trying to keep.
Apiata: we're already committed here, and they're too strategically useful to give up anyway.
Indorians: see above, plus the added caveat of their space occupying a narrow distance right between us and the Cardies.
Dawiar: these guys are at war with an affiliate of ours, and they're right up against our border. We can't let them stay in the Cardie sphere of influence. Its tricky, since the Cardassians have already courted them, but I don't think we can afford to let them keep this one.
Qloath: right in the middle of the contested area, and we have no current interests with them. That said, they're a fellow culture of explorers and it would be a shame to not incorporate them.
Seyek: as above, plus the added factor of their society being somewhat unpalatable by our standards (possibly moreso than the Apiata).
Graetaria: they're uncomfortably near our border, but they're also nonviolent so its doubtful the Cardassians would put them up to mischief.
Yrillians: we know pretty much nothing about these guys, but they're in the same boat as the Graetaria.
Sydraxians: if we're going to throw the Cardassians a bone or two in the name of appeasement, then we shouldn't tug at this one...especially since we'll be trying to take the Dawiar.
I'm thinking that we can afford to let the spoonheads keep the Sydraxians, Yrillians, Graetarians, and Seyek, if we must appease them. I'd rather keep the Qloath if at all possible, based on what we know of them so far, but if we lose them its not the end of the world.
...alternatively, we could stall for a few more years, build up our fleet, and then affiliate with all of them after letting the Cardassian Union's accumulated aggressions fall back upon it in a literal rain of antimatter. That could also be nice.