I don't mind authors doing this sort of thing and actually think more people should. Basically, there's no point to trying to ape H.P. Lovecraft's prose but much benefit to adding your own spin on his universe. It's why I enjoy the works of Brian Lumley's TITUS CROW, Peter Cline's 13 and THE FOLD, Matthew Davenport's ANDREW DORAN series, and David Hambling's HARRY STUBBS series. I admit, I'm biased since I also wrote CTHULHU ARMAGEDDON with this sort of thing in mind.
The premise of the Innsmouth Legacy is the adventures of Aphra Marsha. Aphra is one of the only two survivors of the camps where the population was herded after the events of THE SHADOW OVER INNSMOUTH. This idea was actually done before with THE DOOM THAT CAME TO INNSMOUTH by McNaughton but his story took a traditional view that the Deep Ones, victim of a horrible crime or not, were still an evil cult. This group of Deep Ones is entirely innocent of the blood libel they have been accused of.
The first book had Aphra exploring Miskatonic University and the Innsmouth ruins while dueling with both the Yith and FBI. The sequel takes Aphra and her brother Caleb on a quest to New York (as well as Red Hook) in order to find missing members of the Innsmouth Legacy (a.k.a "mistborn"). Along the way, they encounter the Mi-Go who provide Aphra with a different perspective on the religion she's grown up revering.
I really enjoyed this novel and hope Ruthanna Emrys continues to write books in the setting. While it's a bit iffy to find so many of the Mythos creatures made harmless and good intentioned, she still manages to make some of them quite terrifying. The Yith (also the Elder Race in this version) are also a people she reveres but this book highlights what a vicious and evil race their actions actually make them to being. The K'nyanians (from "The Mound") are also revealed to be even worse than Lovecraft portrayed them.
I also like how Ruthanna Emrys plays with the themes of prejudice as Aphra Marsh proves to be outstandingly bigoted and close minded against the Mi-Go. The prospect of defying fate, of exploring the galaxy, and many things we tend to think of as positive are all things that horrify her. She can't get into the mindset of someone who doesn't view the Earth's oceans as the "be end all" of existence.
I also like the follow up from events in WINTER TIDE with the apexia of Mary, Professor Turnbull struggling to get her life back in order, and Audrey's love of Aphra that she remains oblivious too. It seems very likely Aphra is asexual with no interest in mating beyond reproduction (even then that's because she's being pressured into carrying on the Innsmouth legacy) and that's something you don't see very often in books. I also like how FBI Agent Ron Spector is caught between his desire to protect the United States from supernatural threats and his friendship with Aphra (who is actively hostile to the United States for obvious reasons).
In conclusion, I really like this story and think fans of Lovecraft will enjoy it if they don't mind switching genres. It's not horror and it's not a particularly "alien" version of the Mythos but it's still a very good take on Lovecraft's work which I enjoyed for its own sake.