I say, go ahead, give it your best shot.
The idea of "if terms are properly defined" would be at the heart of debate. I think you are saying if terms are allowed to be defined in a particular way.
We experience the world as sensations stored in memory, interpreted as mind. Additionally, memory harbours all those impressions that are *about* the world: judgements of all sorts, that result in assumptions, measures, values, biases, predictions, etc., that also make up the world. A picture of the world independent of us. Reality.
"Real" refers to truth, which is to say that its affirmation is going to promote an agreeable, sensical, and orderly picture of the world. To say that Bigfoot is real is to say that Bigfoot truely exists... Which is to say that "truely" is the manner in which Bigfoot exists. *That* Bigfoot exists is assumed in assessing the *manner* in which it exists: real or unreal.
Existence refers to thingliness. Bigfoot gets to be a thing as long as we need to assess the manner in which he exists. (The implication of "...exists to a mind" is a given.) When we've no need to think anything about Bigfoot, he is no longer a thing... Until we think of Bigfoot again. Existence is affirmed each time we think *about* a thing.
Things exist. Existence is nothing more than things.
(The OP refers to "realism," which is when we invest belief in that picture of the world independent of us, and imagine that thingliness persists.)
Similarly, that Bigfoot is unreal indicates a manner in which Bigfoot exists, one that doesn't fit into the big picture of orderliness. The big picture that comprises the world to each of us, composed on the canvas of the mind, is painted in truth/untruth.
As an example, "real" is the truth delivered to mind directly through the senses: the taste of an apple, the touch of another person. "Real" is truth deduced by mind with unbreakable correctness: the solidity of the ground under your step, or the "up-ness" of the sky. "Real" is truth that is fickle, as immediate and impermanent as truth itself.
I think for this type of debate, they are fairly close to the same thing. Otherwise, it then becomes a matter of "does this really exist?" Cause, one could say "if terms are properly defined, one can prove the existence of God." But denying or doubting certain definitions, I think would thrust the matter into contentious debate. Well, at least as much of my experience on RF has shown to be.
The addition of the word "really" adds nothing to "Does this exist?" because you're asking to be told the truth. I hope.
I'd come back to my conviction that we exist (physically) as illusion. If "we exist as illusion" equals "we exist," then I would agree that we can probably be proven. But leaving off the 'as illusion' part would mean to me anything currently in the illusion domain also "does most certainly exist." Pink unicorns certainly do exist.
It's only "illusion" if you take what is real and exists to be more than they are (realism). Otherwise, it is all that existence always has been.
Everything exists in some manner--existence itself is not a manner. Pink unicorns exist as an example conjured to demonstrate illusion, or as a fantasy, or as an imagining, or as an actuality, etc. Their existence, their thingliness, is not questionable, else we couldn't even talk about them. It's not their existence that is questionable, but the manner of their existence, no matter that it is left unsaid when a person asks, "Does this thing exist?" The manner is still implied there: actual, true, or real.