I'm loving your fic recs so much. You've given me so much new reading matter, thank you! You seem like the one to ask. Do you know of any fics covering Sherlock's time dismantling Moriarty's web?

Hey nonny, I do know of a few fics that follow or touch on Sherlock’s time away after the fall.  Enjoy! :)

Sherlock on Hiatus - Hunting Moriarty’s Web

Vegas High by pennypaperbrain, 6 k, teen.
Undercover after Reichenbach, tracking the snipers who threatened his friends,
Sherlock has one thing left he can depend on: his mind. But when he faces
making his first kill, alone among the mad excesses of Las Vegas, the pressure
turns out to be greater than even he can endure without John beside him. (Part
of Four Corners of the Western World.)

Against the Rest of the World
by
SilentAuror, 151 k, explicit. Sherlock escapes torture in a cell in Turkey to
return to London before he manages to destroy all of Moriarty’s network. John
is engaged, but choses to come with him to complete the mission. .
Pre-relationship to relationship.  This
has action/adventure like a spy novel, but the incandescent sex scenes were the
draw for me!

A River Without Banks by
Chryse, 203 k, explicit. This story is worlds within worlds. Sherlock uses a
time traveling device to go back into his past, rejoining his consciousness to
that era to redo key points in his life. Over and over, Sherlock tries to find
the change that will defeat Moriarty once and for all. This fic has it all.
Warnings for torture and rape.

457 Days by
221b_careful_what_you_wish_for, 2 k, mature. While Sherlock is traveling during
his two years away, hunting down Moriarty’s web, he finds himself ill, holed up
somewhere with fever. Thoughts and regrets come spilling down to keep him
company.

Last Call at the Homesick Pub by Chryse, 3 k,
teen and up. This is a lovely bittersweet look at Sherlock as he traveled in
disguise around the globe for two years hunting Moriarty’s web. Just for a few
weeks, Sherlock plays the fiddle with an expat Irish band at a pub in some
foreign city far from home.

The Sigerson Letters by h3rring, makokitten,
WIP, mature. A month after the fall, John begins receiving emails from a young
fan who calls himself Jeremy Sigerson, a fan who seems determined to keep an
eye on John and single-handedly spread the truth about Sherlock Holmes and
James Moriarty. But that’s surely a task too monumental for one man, isn’t it?
Unless that man is… (While this fic has been abandoned, I enjoyed it too much
not to rec it.)

Letters series by
earlgreytea68 – 5 parts. During Sherlock’s absence after Reichenbach, he writes
John letters than he never intends to send. When he fears for his true death,
he mails them off. John tracks him down. Angst, romance, and crazy all wrapped
together.

Landscape with the fall of Icarus by caitlinfairchild, 4 k, teen and up. This is a very clever “fill
in the blanks” fic that describes what happens to Sherlock at the beginning of
series 3. Some torture, and PTSD, and Mycroft to the rescue. So well done!