I have no interest in trying to prove the existance of a Matrix. I certainly don’t have evidence that one exists, nor do I have evidence that one does not exist.
I think you’re missing the epistemological point here, a crucial one. You don’t need evidence that it doesn’t exist. This is a logical fallacy, the proof of a negative. It is impossible. Only positive statements need proof, and only positive statements can be proven. So I don’t need to tear myself between whether I can or cannot prove this imaginary Matrix. I trust my eyes, by default. If someone has a positive statement for the existence of a Matrix or that my brain is in a vat, then let them come forth and present their arguments. That is the proper epistemological stance to take here. This thought experiment only works if you’re willing to expect proofs of a negative.
Again, saying that the methods a major academic branch work with are a mockery is not a good way to get them to accept your philosophy. Not all philosophers in academia are useless. The department at my university contained Tara Smith, perhaps the most well known objectivist academic philosopher, as well as a highly-respected classics and classical philosophy section. These are people who have respect for what philosophy is supposed to be
Well then we disagree not only on our means but our goals. It is not my intention to convince these people; I have met enough of them to know that they are lost beyond all hope. And I don’t believe they “have respect for what philosophy is supposed to be”. They like their imaginary mind games and thought experiments, all the while they neglect to prove the most elementary facts that men require to live, and in fact frequently work to undermine them and to poison human existence. It is these people that you will find convincing everyone that free will doesn’t exist, that Marxism (or some form of state control) is the moral ideal, that reason is “limited”, and that who can know whether we exist anyway. No thank you. With friends like these, who needs enemies?
On the other hand, I would not rush to lump the classics into the same category; classics as a profession is also rotten, but not nearly as much, and it is still largely weighed down by having to be anchored in fixed texts which will never change, and that limits how much damage can be done to the field. Still, even with this anchorage the Classics now outputs articles such as “Gay Homer” and “Concordia Discors in Aristophanes’ Clouds” – in other words, mindless gibberish that not only teaches the current generation nothing about the classics, but actively serves to neglect and undermine that education (by not wanting to prioritize traditional Western values as anything important, or worth keeping up and teaching to the next generation).
As you can see from my (very early) posts here and also on The Forum, I have a very avid and long-standing passion both for classics and philosophy (I have a BA in Philosophy). But I hold out no hope for lunatics who would rather live in their cocoon and poison the lives of everyone around them. Bitter but true! I’d rather live my life in pursuit of my values 
Possibility is like the first, low, hurdle on the track. A claim doesn’t have to have much to it to get past the hurdle of possibility. It simply cannot contradict known facts, the laws of physical reality, or be internally logically inconsistent.
No, you’re taking the metaphor of a ladder too far, so much so that the first rung is not even above the ground! That is all we are asking, that if you see this as a ladder, then even the first step must be above the ground, and be a positive argument. Even if it is a very low first step, no matter how little it is above the ground, it still is above ground, and it still needs some positive statement in favor of it, no matter how inconsequential. This is a foundation for logic, that you cannot disprove a negative, and this principle is approximately 2,300 years old. Surely they have taught this idea in all of the hallowed academic philosophy courses you’ve been telling me about?