Arguments shifting the burden of proof are rarely, if ever, productive except when very technical. So it's fair to assume that both sides seriously cosidering this question have some burden of proof.
My comments on the nature of an ad-hoc argument still stand and I will repeat them.
In science, a theory or modification to a theory is not ad-hoc if the theory or modification proposes some new falsifiable way to be real. In philosophy an argument or rejoinder is not ad-hoc if either evidence or at least some new logically coherent independant argument can be offered in support.
If you really do reject my assumptions then there can be no recourse because to reject these is to say no theory should be accepted. I lean towards logical empiricism myself but spoke carefully not to fall into the trap of claiming "You should only accept as true what is true by definition objectively true by verification." Why? Because that axiom is self defeating since it is neither objectively true nor is true by definition. I've written five pages so far which I haven't posted and isn't nearly done on the underpinning theories around a single simple evolutionary example. I will continue, complete and post them here if you have some normative (ought/should) based belief about accepting a theory as probably true.
It is not my fault IF you are too lazy too clearly state your arguments.
It actually is your fault if you refuse, so as to maintain the maximum possible inscrutability of belief, to give any inclination of productive starting ground - and furthermore refuse to accept or acknowledge the most basic and carefully worded assumptions necessary for meaningful discourse. In essence, you could require the presentation of a composite Theory Of Everything. A probabilistic argument is well beyond the scope of this discussion.
Again, I really think we should leave the neanderthal example. Your rebuttal was no more specific than mine and is full of just as many holes. We're evidently still talking past each other on that. Yes, of course a past genome would be impossible beyond the maximum shelf life of genetic material. But when preserved, such suffices and has been used before. Agree or disagree? Now, your statement about the makeup of the current genetic range is false according to geneticists. Mine reflected the current consensus opinion that given a genome, a geneticists could accurately say with a stated margin of error if a sample was or was not within the range of modern humans. Either we're talking past each other or you're asking me to prove things which are in the public domain and are only secondarily or tertiarily related to my position.
You then proceeded to make several claims about the fossil record and expectations about it. This is yet another related topic, but here you make at least one statement that is sufficiently specific for me to actually construct a response to.
You claim that if evolution were true, we should have found more fossils than we have and that the distribution should look differntly than it does.
I'd be happy to defend, specifically: The fossil record constitutes evidence which supports the theory of common decent.
If you first tell me whether you accept the geological column theory and the techtonic plate theory of geology you could save us both a lot of time. If you don't, I'll expect you to say why not - since again these are in the public domain and are only secondarily related to my position. You could add in dating methods to that list while we're at it. And beneath that the theory of radiometric decay, soil sublimation, depository transitions and the compressive production of soil types...the mineral infiltration and replacement of biological bone material...
There is a logical fallacy called the Burden of Proof fallacy whereby a position is maintained through unrealistically high standards of evidence. Generally when you say there should be more or less of something to constitute evidence this has to either be compared to a quantifiable deficiency, another set of disconfirming observations of the same phenomena, or else there must be some other theory which better fits the data. Otherwise you have no rational reason to expect more. You could want more, but it is irrational to reject a theory because of how much evidence you want. If you disagree with my early assumptions, you probably don't agree to that.