I kind of feel like です is more personal, more set, whereas がある (or はある) is more distanced, more nebulous or open to change. (I'm actually more comfortable with はある; I think it sounds a bit more correct, or likely.)
Consider です. 青いです means "It is blue", period, and that is a fact. By contrast, using ある instead of です implies a little less personal investment in the statement, to me.
Let's consider そのつもりです and そのつもりはあります.
If these statements are in the first person, then そのつもりです implies (to me) a confidence that it WILL happen, while そのつもりはあります sounds a little less confident (or more open to change) or just more distanced (perhaps in an effort to be humble).
If someone were looking to change your mind about plans you have, and you answered そのつもりです, it would sound to me like you're against changing your plans, or (at worst) in favor of your plans and not sure why you should change them. If you answered そのつもりはあります, though, it would sound a little more receptive, to me.
If these statements are in the third person (a third party is the subject), then そのつもりです implies (to me) confidence that those are the other person's plans, while そのつもりはあります might imply that you believe those to be their plans, but perhaps you're not greatly familiar with those plans, or perhaps not greatly familiar with the person and don't feel comfortable speaking so strongly for the other person (again, humility you could call it).
As for the negative examples you gave, I feel like they're just talking about separate things. (I'm going to substitute その for ～する and は for が again, for simplicity/my comfort.)
(I) don't have those plans. OR Those are not (my) plans.
Those are not (my) plans.
Now, the second translation for the former looks like the latter, but..."my plans" in the former is "plans that I have", whereas "my plans" in the latter is "THE plans that I have".
The former is expressing: you suggested a plan, and I don't have that plan (though I may have other plans). The latter is expressing: you suggested that I have plans and that they are X, but the plans I have are NOT X.
But, of course, the disclaimer...I'm not a native speaker, so I could just be imagining some of this. But I guess that's in part what the voting system and comments are for. Speak up, Stack Exchange!