"There are plenty of processes that really are explainable as random and/or non-directed events."
Only disagreement I have with your post is right here, even then it may seem a small (yet could be vital) piece.
I must correct that statement by editing in that "There are plenty of processes that could be explainable as random and/or non-directed events, or simply we have not observed the director scientifically yet"
You address this later in your post (by stating In order to arrive at proof of design, one must find some method by which to discriminate between design and random circumstance.), so I'm sure you don't disagree entirely, but I just felt like adding the qualifier.
If we can't discern random events from design, how can we claim that there are indeed inherently random or designed events?
Good question. I think the answer is that we probably can tell the difference, at least some of the time.
We can easily recognize human-manufactured things, for instance ... even if you find them off in the middle of nowhere, and even if you don't know what they are for. Perhaps we have enough experience with such things that we can recognize the hallmarks of human handiwork.... And perhaps as we become more able to manipulate things at the cellular level and below, we can begin to recognize design (or not) there, too. I think the fundamental requirement would be to gain an understanding of the processes required for a particular design.
Perhaps the same question could be posed to the SETI folks: how would they infer that a signal came from an intelligent source? Seems to me that the problems are have a lot of similarities.
It was a mind-croak to them.