[A]m I rational in thinking that there is a desk before me when I seem to see it?
Yes. That is rational. Firstly, desks are known to exist. People have jobs making desks. People buy desks. People use desks. It is true that you could be completely insane and think there is a desk where there is not. However, then one needs to explain what keeps your stuff from falling and why everybody else similarly believes that such a desk exists. It becomes much less rational to disbelieve in the desk than to believe in the desk.
If so, what grounds are there to suppose that mystic experiences are not also legitimate ways of knowing?
The same grounds which existed for concluding that the desk existed. Do people have jobs making mystic experiences (outside of drug dealers)? Do people buy mystic experience? Do other people share an exact same mystic experience (do they also see the walls melting)? Can we test these things and find the results consistent with other things in existence? Does the absence of mystic experience leave a number of hard lingering questions? It does not become less rational to disbelieve. In such a situation, belief becomes clearly the irrational path.
Why assume that empirical investigation is the only way reality can be grasped?
Because 'empirical' deals with reality. Should we attempt to grasp reality by what exists in reality or things which do not exist in reality? Asking why we should use empirical investigation to discern reality is like asking why we should aim for the hoop when we want to make a basket.
Secondly, there are certain fruits of these labors. For example, the internet functions with the aid of a number physical properties and quantum phenomenon. We didn't learn about these by investigating how ghosts manage to push light through fine strands of glass? How long should we have spend testing for goblins within transistors?
Investigations into the supernatural, into gods and ghosts, horoscopes and rabbit feet have produced nothing. They have *never* given us a greater understanding of reality. We have never used ufology to make a better mousetrap or speed up a computer, only empirical investigations do that.
In short, we should look to reality when we intend to grasp reality. Because, it's the only thing that has ever worked and produced repeatable results; results which have given us all the technology we use everyday and all the understanding about the world we have today.
Damn I was good.