I suppose I agree with everything you have said except

An abstract object, pretty much by the definition of "abstract" (which means, "extracted from"), does not exist. It was abstracted from something which did exist, but it did not exist before some mind abstracted it (or it would not have been necessary to abstract it in the first place). — Mariner

The problem I have with this is the idea that the existence of anything , abstract or not, the perhaps 'presence' of the noema in hyle, does not exist in the strict sense but has a borrowed existence. I don't agree, because I think there are instincts of fesr and anxiety within us that relate to imaginary objects, and beings of which do not in a sense 'exist' but have the notation of existence. I think, on the contrary, that existence itself is a demarcation regarding what we can have control over by means of the intellect; all other being is in the mode of unapprehendable, de facto, a priori, etc.

If this is true, then this is not — Mariner

I know dreams and hallucinations and such, like this discussion.
We already have verbiage like imaginary/fictional versus real, and the likes of that mentioned in the post above.
I'd have to say it works better than "being" versus "existence", but maybe that's just me.