couple of points
1. Naturalistic mechanisms can be ID.
2. It would be interesting to begin to test for QM effects, or other areas, to see if there is some principles and predetermined dispositions within the chemistry of the DNA.
As far as experiments, this experiment in the OP works nicely. It demonstrates non-randomness in mutations. Non-randmoness in mutations, is by definition, a move away from evolutionary models, and is indicative of design.
By the way, not saying one cannot claim that the non-randomness evolved as well, but the more you go back, you are going to, imo, find that the information and design is embedded in the process as a guiding force, and that a closer look at all the evidence in this light is warranted.