Just because they split doesn't make them *too* weak, just drying out. A 3-4" oak runner would be very tough to break for a long time. Hickory would be good. WNY gave the very best, locust if you can find it. I've seen post that have been in the ground for 100 years not rotted out.

What about putting a kicker half way up. You could fasten them to the tree as they pass by on their way to the ground Ladder goes up, kicker comes off the back half way up, of the stringers at an angle on either side of the tree. If that doesn't stiffen up that ladder beyond anything you"d ever need I don't know what would short of concrete steps. If that doesn'r suit you put more kickers on. Do it right and let the extend past the stringers and you can attach a hand rail. The only worry I could see is the fastenerns rotting away.