noAdjectives:
Thanks for an interesting discussion. 
I hope it's as rewarding for you as it is for me!
For sure.
noAdjectives:
Well, not that I have sat down and really studied how we can prove
things, but for the sake of this argument I assume that the scientific
method can prove or disprove a hypothesis, such as "gravity exists". If
"gravity exists" is proven by the SciMeth, then we can call it an
objective fact, and anyone saying "gravity does not exist" is therefor
objectively wrong.
OK, I think this might be the important part (maybe not). SciMeth (I like the abbreviation!) does not prove that gravity exists. What it does is allow the testing of hypothesis. If I hypothesize that gravity does not exist (and design and conduct controlled experiments, etc.), SciMeth will indicate that my hypthesis is incorrect and any theory I propose based on the non-existence of gravity is false.
UPB (which I am familiar with only at the level of having read the book a couple of times), does not make positive claims about morality, just as the scientific method does not make positive claims about reality. It is a process of invalidating false moral claims.
To go a step further (and this might be too far):
As humans capable of functioning in the "real" world, we also *largely* accept that what SciMeth has faced and let pass (ex. theories that include a correct model of gravity) are "True." This indicates that they are closer to objective reality than any competing model that SciMeth has been used to process. Models that lack unicorns, tin pots on the far side of jupiter and god are closer to objective reality than models that posit their existence.
Of course, SciMeth cannot say that unicorns don't exist absolutely, just as it cannot say, absolutely, that I'm not a brain-in-a-tank or a computer simulation. But if we accept (as you say you have), that an objective reality exists and that it is impressing itself upon your senses in a systematic way, then we can say that we "know" that unicorns don't exist.
In the last parallel, UPB cannot say anything if human beings are other than we experience them to be. That is, if there is no objective reality, then it might be that people engage in debate for any number of reasons. Accepting that human beings are a part of objective reality, we can must accept that they engage in debate because they prefer truth to falsehood. Either they want to rid themselves of error by rigorous analysis of their claims, or (less healthy), they need to bolster claims they refuse to accept as false by bullying or working themselves into a state of anger or whatever. The interest is the same in either case, to come away feeling more certain that they are making true claims. If anyone argues against that claim, they must be doing so because of this same preference (it might be via either of the two methods, but the interest is the same). Unless logic is an illusion, or we are brains in tanks, then there is a universal human preference to experience one's beliefs as True.
I felt good about this post up until the last paragraph. I may have misrepresented UPB in some way, so if anyone can help me out, I would appreciate it. But does that make sense?