I just discovered this game and its companion setting book last week.  Low Fantasy Gaming is kind of a strange system, written by a 5e guy trying to make something grittier, rather than an old school gamer trying to make something new, so it feels decidedly less gritty and low fantasy than I'm actually used to.
However, the Midlands setting book is pretty great and contains a lot of material that would complement an AS&SH game.  The setting is human-centric, with five distinct human cultures (three are analogous to England, Roman, Viking, and I'm uncertain about the other two).  The region covers six cities with lots of dangerous wilderness in between, there's a bestiary with some new monsters - demons, slimes, and amphibians mostly - and a nice collection of GM tools including generating taverns and random tavern brawls, region events, and lots of random encounters by geography.
The bulk of the book though (about 200 pages) is the Adventure Frameworks section, which has fifty small adventure seeds.  These are grouped by terrain (city, forest, jungle, etc) and could be dropped in pretty easily into any game.  I haven't read even half of them, but the tone looks like a really good match for Hyperborea.  There's a cult trying to earn the blessing of a silent god by cutting out hearts, a jungle ziggurat built by serpentmen, a coven of prophetic swamp hags to barter with, a great monolith in the snow guarded by an elder elemental.  The cartography and artwork throughout is quite nice too.
Low Fantasy Gaming is free in pdf form, though there's a kickstarter for a deluxe edition going on now.  Midlands is $10 in pdf but might be getting a revamp after the deluxe kickstarter.  It's well worth it at the current state, in my opinion, just for a slew of small adventures to sprinkle around Hyperborea.  I'm surprised I hadn't heard of it before this week, but Low Fantasy Gaming is a pretty horribly generic name and the Midlands setting might have been overshadowed by Glynn Seal's Midderlands.