The funny thing about Inspector Spacetime’s Time Wave was that it started out even vaguer than Doctor Who’s Time War. Back in 2011, all we had to go on was scattered hints about it from Russell T. Davies in the lead-up to "The End of Time" (which hardly showed it at all). I had the idea of substituting an ambiguous word, one that could refer to either something concrete, like a "tidal wave", or abstract, like a "wave function"—plus I liked the loose pun on "crime wave".
Although that sufficed for Stephen Moffat's first three series while he was writing about the Silence, now that he's brought the Time War back to centre stage for the 50th anniversary, we have to flesh out the concept of the Time Wave a bit more. We'll see how exactly Moffat celebrates Doctor Who’s semicentennial, but in the meantime, we can come up with our own way of doing it. Naturally, we can also take the opportunity to critique Moffat as a showrunner, such as his predilection for convoluted plots. For starters, if the Doctor more or less betrayed the Time Lords during the Time War, then Inspector Spacetime would turn that on its head by having the Infinity Knights somehow double-cross the Inspector.
If we had to pitch a storyline to Anthony Bonham Pease, we could propose a sci-fi hybrid of the 2002 Infernal Affairs and Dirty Harry's Magnum Force, for instance: The Infinity Knight High Command assigns the Eighth Inspector to infiltrate a group of renegade fellow space-time officers who are conducting their own private war against the Blorgons. As we see in the webisode "The Twilight of the Inspector", he decides to go undercover as a rogue cop and secretly transforms himself into the Unknown Inspector with the help of the mystic Teman Mothers. After some off-screen adventures, the undercover Inspector finds out that the renegades are plotting to use the monstrous MacGuffin-esque Time Wave to destroy the Blorgons once and for all.
Horrified that Infinity Knights would take the law into their own hands like this, he reports back to the High Command, only to discover that he has been set up. The renegades had deduced the Inspector was actually a mole and went far back in time to sabotage his inquiries. Just after the Big Bang, they had struck a deal with Commissioner Sassafrass when he first established the High Command. Sassafrass then covertly ran the renegades as his own strike team until other members of the High Command became suspicious about unexplained interference in causality—which brings us back to when the Eighth Inspector was recruited to look into them. Their conspiracy, however, is now planning not just to trigger the Time Wave but to frame the Inspector for it as well.
Picking up for the 50th anniversary "The Night of the Inspector" and the Christmas special, the Unknown Inspector must enlist the aid of the Eighth, Ninth, Tenth, and Eleventh Inspectors (IS gets to bring back twice the number of actors as DW, of course). The Inspectors have to struggle with not only the Blorgons and the assorted past foes they recruit, but also the corrupted Commissioner Sassafrass, the renegade Infinity Knights, and the suborned High Command. Meanwhile, the countdown to the Time Wave ticks away, threatening the whole universe. In the end, the only way to prevent the Infinity Knights from going down in history as having been as bad as the Blorgons, if not worse, is for the Unknown Inspector to obliterate both sides, even though this means his taking responsibility for the Time Wave. In the final scene, the past Inspectors return to their own time streams, and the Eleventh Inspector metamorphoses into the Twelfth.
Meantime, though, finalising the Twelfth Inspector's casting is another topic to work on. Our a placeholder has been sufficient for the past few months but otherwise hasn't caught the Internet's fancy, so perhaps it's also time address that...