Players with a 15 str are supposed to be able to make the jump but because it's slightly inclined jumping TO the keep, there's a DC10 athletics check that incurs damage on a fail.

What should players with str's below 15 do?  Use rope?  Is rope an automatic success?  Grappling Hook?  What are the mechanics of using a grappling hook?

Would climbing down, swimming the moat, climbing up be an option?  That might work out to be a couple of athletics checks for the climbing parts, with or without a rope.  And a threat of normal falling damage on fails.

In any case, I let the lower str characters all attempt the jump and had the athletics check cover both the attempt and potentially damaging landing.

Any thoughts?

or this: Jump

Not familiar with the adventure, but I can't see why a rope and grappling hook wouldn't work. If players have two ropes and grappling hooks they could even take 20 on the roll to hook it and lose a rope and hook (for the "1" result). When it comes to stuff like that I have the players make a Dex check for the throw, adding their proficiency bonus if they're proficient in the climbing kit.

Since I don't know the adventure, couldn't tell you about the other options.

Anything that works! There still might be a check for using rope or something else depending on the conditions, etc. But that's really your call.

You could always place some boards across the gap.