I've heard of Hoyle's speculation, the fanciful sci-fi notions of space aliens, yada yada. My point would be I just don't consider any "search" for "a designer" to be a proper scientific question at all. Assuming the designer were God, it's not like you're gonna get God down into the laboratory so that you can "observe" Him. But this would be required of science, if indeed it wanted to ask this question, which I strongly doubt it does anyway.
The point is, though you cannot "handle" the putative designer, you can "handle" the putative evidence of design. For it can be directly observed. That is susceptible to scientific test in a way that the designer never (in all probability) could be.
I really liked your astute observation: "What if the necessary evidence requires better access to a dimension that we have little access to at this point." That seems eminently to be the case. But again, if the designer were God (Who is "extra-dimensional" at least in the sense that the heavenly realm is no part of material reality), regardless of how many new dimensions might be discovered, I expect that God would not be "found" in any of them. In principle.
So it's silly to go chasing after the designer. The problem before us is to look at/for the design; and let each person who wishes to engage in philosophical or theological reverie go right ahead and try to figure out the problem of the designer if he has an inclination to do so. Or not as the case may be. The point is: Look at the world. That's all science can do, anyway.
A house is evidence of the architect, even though the architect is not in it. Creation reeks of a designer, and those who study it with this thought in mind are the ones who make the most progress unlocking it's secrets.
In other words, one does not reverse-engineer a thing unless they believe it was engineered in the first place.
This isn't a response to you as much as an amplification, from a different position, of what you are already saying.
Thanks for the pings, btw.