If it's that corner you're worried about move the drain pipe! That bank is steep, but those mature trees don't have exposed roots, so it's relatively stable. Stop eroding it with your roof drainage by piping the drainage all the way to the bottom.
I would take a hard look at the flows in the bottom of that swale and see if they're erosive, and if so, I'd consider changes to the flow in the swale to prevent them from being so erosive. Otherwise all the foundation measures in the world won't help as the crevice continues to widen.
Hydrology, Drainage Analysis, Flood Studies, and Complex Stormwater Litigation for Atlanta and the South East -
Armor the natural swale (rip rap) that has formed down to the bottom of the gulley and divert all stormwater to the swale. Use some temporary erosion control matting and seeding to stabilize the existing bank. Install a gutter system and downspout that discharges to the amored swale. Then work on the foundation. I would save the building, as your permitting agency will never issue a building permit in that same vicinity without a ton of engineering work.
I recommend having an experienced Geotechnical engineer come out to look at the situation. This may not be as bad as you might think, but a geotechnical proffessional will be able to help you with the extent and nature of this problem. Good luck.
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