I guess it depends on everyone's definition of fanfiction and their view of: Is Fanfiction Literature? I guess I've always felt fanfiction is a hobby where people can extend a world they love, but not something publishable. I've always imagined a retelling of a classic tale like retelling P&P in Bridget Jone's Diary wouldn't fall under fanfiction because Pride & Predjudice is now in the public domain.
I wouldn't say that
Bridget Jones's Diary is not fanfiction because
Pride and Prejudice is in the public domain. I'd say that it's not fanfiction because they're barely related.
Sorry this has gotten off-track. I think when you take a classic character and use them in a novel, you have to think mainly about how other fans have used that character and what the fanbase is going to want, as well as who you're writing it for.
If you want to please people who enjoy Sherlock Holmes as a character, then you need to leave the elements people like about him intact. Some changes you can get away with (like how some people write him as asexual, and others write him as being attracted to Irene Alder).
I wrote fanfiction as a teenager and recently went back to write one last fic for an author I adore. I wouldn't say it's at all lesser or bad. It just requires a different skillset, and there's a different set of expectations in place. Like, here, how the OP has to pay attention to what other people will think of his/her changes.