Everyone in the ID movement is welcome to look for evidence of genetic engineering. It's not even expensive since genome data is online.
When humans engineer organisms -- and I presume you would include this as an example of intelligent design -- they tend to insert genes from one species to another, even crossing the lines at the level of kingdom.
This results in organisms that do not fit in a nested hierarchy. So ID supporters might spend their time looking for breaks in the nested hierarchy. ERVs would be a logical starting place.
Silly statement. Why must ID be a movement? Is "evolutionary theory" a "movement," too?
That said, I thank you for summarizing so neatly the testing approach that I had tried to state before.
Clearly, then, you would have to agree that the "ID hypothesis is not testable" canard is no longer valid, at least not as a general statement.
The techniques of genetic engineering (which is a form of "intelligent design," just as you said) are such that the signs of similar activities by "unknown agents" might be recognizable.