It's not a straw man if there are people willing to make the claim, regardless of its existence... and plenty here have.
If you meant random to apply to the event, mutagenesis, then there is a possibility that mutagenesis may, in some instances (like those you propose) appear random but may actually be biased by epigenetic (environmental) pressures. This is okay with me, because either way supports you contention.
If said mutagenesis is truly endogenous, it may be also truly random or be driven by endogenous events hitherto undiscovered and deviate somewhat from randomness and yet still appear random. Either way, this would not detract from your position at this stage of the game.
What may be occurring is that there are unknown events that are not recognizable as selective pressures--either endogenous or exogenous--that are producing mutagenesis. Furthermore, this mutagenesis would be difficult to infer from inspecting paleontological data or anatomical comparisons.
An aside: Many scientists who promote evolutionary theory resort to a circular reasoning fault inasmuch as they proclaim an anatomical structure to have evolved as an adaptive evolutionary response. When, in fact, the structure may well be: 1. irrelevant in that it did not impede adaption 2. an atavistic throwback or vestigial structure 3. or one that was circumvented by other adaptations. The circularity comes in when they are asked to explain and they resort to: "The structure exists because it evolved and it evolved because it exists." "Neither" is also a distinct possibility.
Nevertheless, a process of mutagenesis that appears to be outside the vagaries of known selective pressures, one that seems to occur endogenously (that is without regard to exogenous factors) and one that is rather vigorous (and thus accounts for rapidity, variety and "surprises" in evolution) may well operating as the mystery behind those aspects of evolution which remain enigmatic.